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let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | i just have a positive 7 . and now let me just draw my little funky synthetic division operator-looking symbol . and remember , the type of synthetic division we 're doing , it only applies when we are dividing by an x plus or minus something . | and also , where did the `` operation '' symbol come from ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and now we 're ready to perform our synthetic division . so we 'll bring down this 2 and then multiply the 2 times the 3 . 2 time 3 gives us 6 . 0 plus 6 is 6 . | the denominator is 3x-2 would i still put positive 2 at the same place where sal puts the 3 0 in the video or does the 3x affect this ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | so does this mean that every time you use synthetic division , there will be a remainder ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | the x^5 term was 2 , and the x^4 term was 0 ( which became 6 ) , so how did two become the x^4 and 6 the x^3 ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | multiply that times 3 . the numbers are getting kind of large now . so that 's going to be what ? | i mean why ca n't we just use the number beside the x and then subtract the numbers on the second row from the numbers on the first row instead of add the two rows numbers altogether ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | so it 's really 0x to the fourth . so i 'll put a 0 as the coefficient for the x to the fourth term . and then i have a negative 1 times x to the third . | sal says that the coefficient to the x^4 term is 0 , would n't it be actually 1 ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | how would you use synthetic division to divide a complex polynomial with a complex binomial ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and you add 480 to 7 , and you get 487 . and you can think of it , i only have one term or one number to the left-hand side of this bar here . or i 'm just doing the standard , traditional x plus or minus something version of synthetic division , i should say . | so the last term is always the remainder ( if we have one ) right ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and so you 're going to have plus 160 plus 487 over x minus 3 . now this is our x term . so it 's going to be 54x plus all of this . | why is the last term of the polynomial the only one that is divided by x and another number ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | how would you find the zeros of a function using synthetic division ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | if i were to divide 3x^2 - 4x + 7 by x - 1 , i get 3x -1 with a remainder of 6 with long division and 3x - 7 with a remainder of 14 , can someone explain what i 'm doing wrong ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | is there a way to factorise a polynomial with a degree greater than 2 ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and the process we show -- there 's other ways of doing it -- is you take the negative of this . so the negative of negative 3 is positive 3 . and now we 're ready to perform our synthetic division . | what would happen if there was a coefficient next to x-3 example 2x-3 at the denominator ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . | do i have to learn synthetic division if i know how to do long division ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | but there are other videos why we explain why . and it can be fast and convenient and paper saving very often , like you see right here . but then we have our final answer . | is there any difference between the two besides speed and space saving ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | negative 2 times x . and then i have a constant term , or zero degree term , of 7 . i just have a positive 7 . | why did you use the zero ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | negative 2 times x . and then i have a constant term , or zero degree term , of 7 . i just have a positive 7 . | hi , i was wondering why you would take the opposite of the constant in the denominator , since does n't that mean we are dividing by zero ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | how do you use synthetic division when using binomials ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | so then i have my x to the fourth term . so it is 2x to the fourth . and we are done . | why does 2x^5 become 2x^4 at the end of the video ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | it 's going to be -- and let me work backwards . so i 'll start with our remainder . so our remainder is 487 . and it 's going to be 487 over x minus 3 . | how do you apply the remainder theorem ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | multiply that times 3 . the numbers are getting kind of large now . so that 's going to be what ? | how would i divide synthetically if i have complex numbers ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and you add 480 to 7 , and you get 487 . and you can think of it , i only have one term or one number to the left-hand side of this bar here . or i 'm just doing the standard , traditional x plus or minus something version of synthetic division , i should say . | how you find the number you divide from the polynomial equation ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | negative 2 times x . and then i have a constant term , or zero degree term , of 7 . i just have a positive 7 . | where does the zero come from ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | it 's going to be -- and let me work backwards . so i 'll start with our remainder . so our remainder is 487 . and it 's going to be 487 over x minus 3 . | how do u do remainder theorem in polynomial functions ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and the process we show -- there 's other ways of doing it -- is you take the negative of this . so the negative of negative 3 is positive 3 . and now we 're ready to perform our synthetic division . | what does sign of remainder - and + signify , it was - ( negative ) on previous and + now , how ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | 2 time 3 gives us 6 . 0 plus 6 is 6 . and then we multiply that times the 3 , and we get positive 18 . | where did the zero ( 0 ) came from ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | i do n't know how to do this type , no one seems to cover irrational numbers : x^4+2*squareroot ( 2 ) *x^3+4x^2+2*squareroot ( 2 ) *x+1 i know the answer is ( x^2+squareroot ( 2 ) *x+1 ) ^2 but how do you find the factors or how do you divide with synthetic division to get the perfect square factored form ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | this only works when we have x plus or minus something . in this case we have x minus 3 . so we have the negative 3 here . | what do i do if there is no x + 3 being divided and i have to find a number to use ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | it 's going to be -- and let me work backwards . so i 'll start with our remainder . so our remainder is 487 . and it 's going to be 487 over x minus 3 . | how would you graph the remainder in a calculator with the rest of the equation ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a negative 1 times x to the third . and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | so how would you go about this problem if ( x-3 ) was ( x^3 - x^2 ) ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and the process we show -- there 's other ways of doing it -- is you take the negative of this . so the negative of negative 3 is positive 3 . and now we 're ready to perform our synthetic division . | how about ... x - 3 becomes 3x - 3 ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | negative 2 times x . and then i have a constant term , or zero degree term , of 7 . i just have a positive 7 . | why is the answer a 4th degree polynomial when the question is a 5th degree ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | where does the name 'synthetic division ' come from ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | in college i took a situation in which we divide f ( x ) / ( x-a ) ( x-b ) by using synthetic division .. is there a lesson about it here ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then we multiply that times the 3 , and we get positive 18 . negative 1 plus 18 is 17 . multiply that times the 3 . | how would i synthetically divide if my divisor variable had an exponential of more than 1 or a co-efficient ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then we multiply that times the 3 , and we get positive 18 . negative 1 plus 18 is 17 . multiply that times the 3 . | what happens if you are dividing by a polynomial with a degree higher than 1 or more than two terms ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | 17 times 3 is 51 . 3 plus 51 is 54 . multiply that times 3 . the numbers are getting kind of large now . | so if you are dividing by x+3 , do you multiply the coefficients by -3 and still add two numbers or subtract ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | this only works when we have x plus or minus something . in this case we have x minus 3 . so we have the negative 3 here . | what do you do when a power of x is missing , say the problem is 5x^3 divided by x-3 , i know that you have to add a 0x2 and a 0x before dividing but do we also need to add a plain old zero as well as one of the coefficents ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | is synthetic division only used for polynomials ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | what i 'm asking is , why did the exponent change ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | why do n't we use the 5th power , 3rd power , 2 powered throughout the video ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and the process we show -- there 's other ways of doing it -- is you take the negative of this . so the negative of negative 3 is positive 3 . and now we 're ready to perform our synthetic division . | if you had an expression like 3x+5 where the coefficient is n't 1 , could you divide the expression by 3 to get x+5/3 and then do synthetic division ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | so when you have x+4 you have to use the opposite of the sign ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | what would you do if you had a problem where it has ( x+2 ) and a -1 as your exponent ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | hod did you get zero as a coefficient when finding the numbers to place for the synthetic division ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | if the x has an exponent else than 1 then the remainder will have x to some power , right ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | then how do we decide what power the remainder 's x should have ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | this only works when we have x plus or minus something . in this case we have x minus 3 . so we have the negative 3 here . | in x+3 you need to substitute x to a number that would result to zero , what if the x has a number in it for example : 5x+3 , how do you find out the divisor if this is the case ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and the process we show -- there 's other ways of doing it -- is you take the negative of this . so the negative of negative 3 is positive 3 . and now we 're ready to perform our synthetic division . | why does the -3 turn into a 3 for dividing ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | 2 time 3 gives us 6 . 0 plus 6 is 6 . and then we multiply that times the 3 , and we get positive 18 . | why was the second number a 0 ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then we multiply that times the 3 , and we get positive 18 . negative 1 plus 18 is 17 . multiply that times the 3 . | how about if the denominator is 3y-1 ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and the process we show -- there 's other ways of doing it -- is you take the negative of this . so the negative of negative 3 is positive 3 . and now we 're ready to perform our synthetic division . | will an expression like 3x-3 divide another expression just as x-3 would ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . | how do we find the factors of a cubic polynomial without long and synthetic division ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | does the polynomial have to be in descending order ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | what if you 're using synthetic division to find a f ( x ) that has x as any number greater than 1 ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | so when you are using synthetic division , are you supposed to subtract or add when doing the carrying down and multiplying over ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | how do you get no solutions for synthetic division ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | what happens when the denominator has polynomials ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | so it 's really 0x to the fourth . so i 'll put a 0 as the coefficient for the x to the fourth term . and then i have a negative 1 times x to the third . | how do you know whether you put an addition or subtraction sign into your solution ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | negative 2 times x . and then i have a constant term , or zero degree term , of 7 . i just have a positive 7 . | is there any way that there would n't be a remainder unless the constant was zero ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and the process we show -- there 's other ways of doing it -- is you take the negative of this . so the negative of negative 3 is positive 3 . and now we 're ready to perform our synthetic division . | why is the 3 on the outside positive suddenly ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | how do you figure out what is below the equation if nothing is there ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | but then we have our final answer . it 's going to be -- and let me work backwards . so i 'll start with our remainder . so our remainder is 487 . and it 's going to be 487 over x minus 3 . | if the remainder is not zero , should i just keep going with the same number i 've been using to synthetically divide ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then i have a positive 3 times x squared . negative 2 times x . and then i have a constant term , or zero degree term , of 7 . | how do you divide a polynomial if the divisor is something like x^2+2x-1 ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . | is there any situation where you would have to use synthetic division instead of standard division ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and you add 480 to 7 , and you get 487 . and you can think of it , i only have one term or one number to the left-hand side of this bar here . or i 'm just doing the standard , traditional x plus or minus something version of synthetic division , i should say . | what is the easiest way to pull out a root thats a whole number ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and remember , the type of synthetic division we 're doing , it only applies when we are dividing by an x plus or minus something . there 's a slightly different process you would have to do if it was 3x or if was negative 1x or if it was 5x squared . this only works when we have x plus or minus something . | just wondering , would this be considered an easier way to divide polynomials ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then finally , 160 times 3 is going to be 480 . and you add 480 to 7 , and you get 487 . and you can think of it , i only have one term or one number to the left-hand side of this bar here . | what is the best place to get pie ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and then finally , 160 times 3 is going to be 480 . and you add 480 to 7 , and you get 487 . and you can think of it , i only have one term or one number to the left-hand side of this bar here . | how do you get the zero in the problem ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | and so you 're going to have plus 160 plus 487 over x minus 3 . now this is our x term . so it 's going to be 54x plus all of this . | what happened to the x^5 term ? |
let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . and now is a good chance to give it a shot , to actuall... | let 's do another synthetic division example . and in another video , we actually have the why this works relative to algebraic long division . but here it 's going to be another just , let 's go through the process of it just so that you get comfortable with it . | is it possible to use synthetic division in a long division problem ? |
hi , i ’ m john green and this is the final episode of crash course : world history , not because we ’ ve reached the end of history but because we ’ ve reached the particular middle where i happen to be living . today we ’ ll be considering whether globalization is a good thing , and along the way we ’ ll try to do so... | anyway , flowers , best wishes , john green aww ... you guys got me flowers for my last episode of world history . okay , let ’ s go to the thought bubble . as worldwide production and consumption increases , we use more resources , especially water and fossil fuels . globalization has made the average human richer , a... | during the thought bubble , he said that the use of lots of fossil fuels leads to climate change , but does n't the use of fossil fuels lead to global warming , not climate change ? |
hi , i ’ m john green and this is the final episode of crash course : world history , not because we ’ ve reached the end of history but because we ’ ve reached the particular middle where i happen to be living . today we ’ ll be considering whether globalization is a good thing , and along the way we ’ ll try to do so... | and while it 's true that many historical forces -- malaria , meteors from space -- are n't human , it 's also true that every human is a historical force . you are changing the world every day . and it is our hope that by looking at the history that was made before us , we can see our own crucial decisions in a broade... | is there some way we can reduce/stop global warming , at home , every day , by doing small things ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | so these $ 4 billion in liabilities , these are loans , maybe from other banks . in fact , probably from other banks . and those loans from other banks , those are assets of other banks . for example , let 's say this is bank a , this is bank b . | why do banks borrow from each other in a cycle like kahn suggested ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | i think you 're starting to see how this gets pretty hairy very fast . so let 's say that bank a , one of its $ 3 billion in assets , is a loan to bank c. and so on bank c 's balance sheet , it 'll say loan from bank a . or so we owe a $ 1 billion . | does bank c still need to pay off the loan ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | and let 's say that someone else , just for fun , just to make this interesting -- i think you can extrapolate and think about how this gets complicated very fast . bank b has borrowed money from bank c. so bank c will have an asset here that says , no i lent money to bank b . fair enough . | why does n't it come to bank c to claim the money bank c owes to a back ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | maybe a billion of these are a loan from bank b . and if this is a loan from bank b , bank b would have an asset called loan to bank a . on bank b 's balance sheet we 're calling this a loan to bank a . | a then would have $ 1b cash to repay bank b , would n't it ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | in fact , probably from other banks . and those loans from other banks , those are assets of other banks . for example , let 's say this is bank a , this is bank b . | also , i have quite a funny idea in my mind : if there is , say , an inter-banks loans , why do n't they cancel out each other 's debt ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | so one situation is they could get a loan from someone . maybe the fed would be willing to take this as collateral . so they would give this as collateral to the fed . | what was the reason and why banks were willing to take on that risk on their asset ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | you go into bankruptcy . and this is what happened to lehman brothers . lehman brothers went into bankruptcy . no sovereign wealth fund , no one else bought the company . | would have been better for the world economy if the fed had saved lehman brothers ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | and you can imagine , now it 's even less likely that when a bank , let 's say that bank d is the next one to go into a dire situation , it 's even less likely that bank d can get a loan from a third bank . because all the banks are getting scared now . all the banks are saying , i 'm not going to loan money to anyone ... | are banks ever aware of who is loaning whom money ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | and let 's say that someone else , just for fun , just to make this interesting -- i think you can extrapolate and think about how this gets complicated very fast . bank b has borrowed money from bank c. so bank c will have an asset here that says , no i lent money to bank b . fair enough . | like would bank b know that bank a was loaning money to c ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | so they would give this as collateral to the fed . maybe the fed will give them a billion dollar loan . and then they can use that to pay bank b . | when sal says , that the fed will give them a billion dollar loan , is he referring to the federal reserve , composed of member banks itself , or the federal government ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | and they probably are doing just fine with the bonuses they 've collected after sourcing these cdos for the past eight years or five years or however long . but what i want to show you in this video is what people are talking about when they say systemic risk . so these $ 4 billion in liabilities , these are loans , ma... | so what is the systemic risk ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | and let 's say that someone else , just for fun , just to make this interesting -- i think you can extrapolate and think about how this gets complicated very fast . bank b has borrowed money from bank c. so bank c will have an asset here that says , no i lent money to bank b . fair enough . | if the debt is owned to bank b , does n't it mean that bank b and c owes each other , so their debts cancel each other out ? |
i think we 're now ready to tackle the big picture and what has our government officials so worried right now . so what i 've done is , i 've just drawn the balance sheets for a bunch of banks . obviously , this is simplified . and i made all of their balance sheets look the same . all of these banks , each of these ki... | and let 's say that someone else , just for fun , just to make this interesting -- i think you can extrapolate and think about how this gets complicated very fast . bank b has borrowed money from bank c. so bank c will have an asset here that says , no i lent money to bank b . fair enough . | bank b loaning to a , and a loaning to c , then c loaning to b ... is this called floating ? |
( piano playing ) dr. steven zucker : we 're looking at one of the great sandro botticelli 's and also one of the most enigmatic , the primavera . dr. beth harris : which means spring . in the center we see venus in her sacred grove looking directly out at us . dr. zucker : the figures in the foreground are parted to a... | dr. zucker : there 's one other figure , which is venus ' son just above her , blindfolded . this is , of course , cupid , who 's about to unleash his arrow on one of the unwitting graces and , of course , he does n't know who he 's going to hit , but we can sort of figure it out . dr. harris : typical of botticelli , ... | what is on the tip of cupid 's arrow ? |
( piano playing ) dr. steven zucker : we 're looking at one of the great sandro botticelli 's and also one of the most enigmatic , the primavera . dr. beth harris : which means spring . in the center we see venus in her sacred grove looking directly out at us . dr. zucker : the figures in the foreground are parted to a... | it 's fabulous and we 're not sure exactly what he 's doing . he 's got a stick in his hand . he may be pushing away the clouds that appear to be coming in from the left . | is this the artist the guy in the movie the pick up artist is referencing whey he uses the line `` you 've got the face of a botticelli ? |
( piano playing ) dr. steven zucker : we 're looking at one of the great sandro botticelli 's and also one of the most enigmatic , the primavera . dr. beth harris : which means spring . in the center we see venus in her sacred grove looking directly out at us . dr. zucker : the figures in the foreground are parted to a... | this is not a painting that 's about linear perspective . there 's a little bit of atmospheric perspective that can be seen in the traces of landscape between the trees , but beyond that this is a very frontal painting . it 's very much a freeze and it very much is referencing what we think might be a literary set of i... | does the audio seem a bit funky ? |
( lively music ) dr. zucker : we 're in the pompidou in paris and we 're looking at l�szl� moholy-nagy . this is a '20 from 1924 . moholy-nagy was a member of the hungarian avant-garde but in 1920 , he comes to dessau , to germany to walter gropius ' bauhaus and takes over the first year program . now , what 's really ... | dr. zucker : well , it 's almost the language of mathematics . this is an abstraction that refers to those things in the purest terms , almost in mathematical terms , as opposed to the representation of those things . ( lively music ) | could art works of this very abstract kind have been influenced by other things outside the art world such as literature ? |
( lively music ) dr. zucker : we 're in the pompidou in paris and we 're looking at l�szl� moholy-nagy . this is a '20 from 1924 . moholy-nagy was a member of the hungarian avant-garde but in 1920 , he comes to dessau , to germany to walter gropius ' bauhaus and takes over the first year program . now , what 's really ... | ( lively music ) dr. zucker : we 're in the pompidou in paris and we 're looking at l�szl� moholy-nagy . this is a '20 from 1924 . | what is the sculpture/painting on the left ? |
we 're told carbon-14 is an element which loses exactly half of its mass every 5730 years . the mass of a sample of carbon-14 can be modeled by a function , m , which depends on its age , t , in years . we measure that the initial mass of a sample of carbon-14 is 741 grams . write a function that models the mass of th... | we 're told carbon-14 is an element which loses exactly half of its mass every 5730 years . the mass of a sample of carbon-14 can be modeled by a function , m , which depends on its age , t , in years . | if carbon-14 's mass gets halved every 5730 years , then would n't carbon-14 never disappear ? |
we 're told carbon-14 is an element which loses exactly half of its mass every 5730 years . the mass of a sample of carbon-14 can be modeled by a function , m , which depends on its age , t , in years . we measure that the initial mass of a sample of carbon-14 is 741 grams . write a function that models the mass of th... | when t is equal to 5730 , this exponent is going to be one , which we want it to be . we 're just gon na multiply our initial value by 1/2 once . when this exponent is two times 5730 , when t is two times 5730 , well then the exponent is going to be two , and we 're gon na multiply by 1/2 twice . | what is the constant value for mercury 194 ? |
we 're told carbon-14 is an element which loses exactly half of its mass every 5730 years . the mass of a sample of carbon-14 can be modeled by a function , m , which depends on its age , t , in years . we measure that the initial mass of a sample of carbon-14 is 741 grams . write a function that models the mass of th... | well , we know at every 5730 years , we lose exactly half of our mass of carbon-14 . every 5730 years . so let 's think about what happens when t is 5730 . | what equation would give us the amount of mercury remaining after t years ? |
we 're told carbon-14 is an element which loses exactly half of its mass every 5730 years . the mass of a sample of carbon-14 can be modeled by a function , m , which depends on its age , t , in years . we measure that the initial mass of a sample of carbon-14 is 741 grams . write a function that models the mass of th... | well , then , it 's gon na be this times 1/2 . so it 's gon na be 741 times 1/2 times 1/2 . so we 're gon na multiply by 1/2 again . | why did n't you multiply 741 by 1.5 instead of 0.5 ? |
the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this ... | here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . | what else could you tell the viewers about understanding place value ? |
the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this ... | the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . | so the 25430 can be more than 2543 although they 're almost the same numbers ? |
the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this ... | in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . | what is the largest place value ? |
the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this ... | the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . | is n't `` and '' only used in decimals and fractions ? |
the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this ... | fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . | how is 25,430 10 times lager than 2543 when 2543 is not in the 10 thousands place ? |
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