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help-10
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Shuri2060
03/16/2022 10:34:04
Q(x) = P(x) - P(5)
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Shuri2060
03/16/2022 10:34:07
how will this help (it wont)
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Shuri2060
03/16/2022 10:34:16
You try it out and see if u get anywhere.
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Shuri2060
03/16/2022 10:34:50
The polynomial R to choose is not complicated, I can assure you
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Hyperlix
03/16/2022 10:36:39
wait isn't $P(5)=(5)^4+a(5)^3+b(5)^2+c(5)+d$?
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TeXit
03/16/2022 10:36:42
**hyperlix26**
https://cdn.discordapp.c…976142237776.png
898441976142237776.png
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Shuri2060
03/16/2022 10:36:52
It is.
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Shuri2060
03/16/2022 10:37:01
a b c d are constants
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 10:37:22
yeah
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a446f8916c9c48a499caa8c8f0fa7a7f
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Hyperlix
03/16/2022 10:37:38
and how would Q(x) = P(x) + R(x) help me?
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Hyperlix
03/16/2022 10:37:50
what's R(x)?
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Shuri2060
03/16/2022 10:37:56
Read what I said
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Hyperlix
03/16/2022 10:38:02
I know what P(x) is
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Shuri2060
03/16/2022 10:38:08
I said **you** have to find a suitable R(x)
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Shuri2060
03/16/2022 10:38:12
that is helpful
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Shuri2060
03/16/2022 10:38:15
That is my hint
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Hyperlix
03/16/2022 10:39:39
idk what the suitable R(x) is, wanted to make it equal to $(5)^4+a(5)^3+b(5)^2+c(5)+d$ but you said it wasn't equal to P(5) so that's not it
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TeXit
03/16/2022 10:39:42
**hyperlix26**
https://cdn.discordapp.c…976142237776.png
898441976142237776.png
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a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:39:50
skdjfnfkiffifofofofkfkfifo
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:40:03
Dont give up before you've even tried
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Hyperlix
03/16/2022 10:40:06
what
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:40:20
oh nvm misread
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Shuri2060
9525
a μ-er
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a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:40:28
I told you though
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Shuri2060
03/16/2022 10:40:34
to find a suitable polynomial R(x)
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:40:46
And I also said it isnt complicated, it is simple
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help-10
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Shuri2060
03/16/2022 10:41:01
Write down a few guesses, see if they could help you any way.
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Shuri2060
03/16/2022 10:43:25
If youre stuck, then say what R have you tried
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898,441,976,142,237,800
Hyperlix
03/16/2022 10:47:06
yeah nope
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Hyperlix
03/16/2022 10:47:20
nothing else makes sense to me except for $(5)^4+a(5)^3+b(5)^2+c(5)+d$
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TeXit
03/16/2022 10:47:22
**hyperlix26**
https://cdn.discordapp.c…976142237776.png
898441976142237776.png
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Hyperlix
03/16/2022 10:47:35
other than that I'm just making stuff up
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Hyperlix
03/16/2022 10:48:28
if R(x) is a polynomial to find, why not make R(x)=Q(x)-P(x)?
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Shuri2060
03/16/2022 10:48:37
that isnt even a choice
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:48:41
of R
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:48:47
Do you understand what a polynomial is?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Hyperlix
03/16/2022 10:48:56
yeah
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help-10
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Shuri2060
03/16/2022 10:49:02
I hinted a polynomial, so please realise it probably isnt a constant
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:49:16
So what example of R could you try
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:49:18
just name one
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:49:21
any
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Hyperlix
03/16/2022 10:49:39
the same as P(x) but it doesn't make sense
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:50:36
...
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:50:44
Tell me an example
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:50:49
of ANY polynomial
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Hyperlix
03/16/2022 10:51:12
P(x) is a polynomial
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 10:51:13
https://cdn.discordapp.c…2926/unknown.png
unknown.png
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0
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:51:31
omg
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:51:44
can you keep it simple?
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help-10
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Hyperlix
03/16/2022 10:51:56
ax+b?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:51:59
if i randomly asked you for an example of a polynomial you wouldnt give me that
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Hyperlix
0041
Hyperlix
false
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:52:02
why the letters???
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Hyperlix
03/16/2022 10:52:12
it still counts right?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:52:13
An explicit example please?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Hyperlix
03/16/2022 10:52:27
2x+7?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:52:31
Yes. Good.
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:52:41
Now I asked you to consider the new polynomial Q(1) = P(x) + 2x+7
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:53:00
What can we say using the given information?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:53:10
It must still be of degree 4
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:53:19
But in particular what is Q(1) and so on
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 10:53:35
1+2+7
1
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help-10
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Hyperlix
03/16/2022 10:53:40
that's Q(1)
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Hyperlix
03/16/2022 10:53:48
which is 10
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:53:52
indeed
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:53:58
and you can compute Q 1 2 3 4
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:53:59
yes?
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help-10
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Hyperlix
03/16/2022 10:54:02
yeah
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 10:54:17
Now my hint was to pick a *nice* R(x)
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help-10
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Shuri2060
03/16/2022 10:54:32
what 'nice' means, try to figure it out
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help-10
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Shuri2060
03/16/2022 10:55:05
I will say now that Q(1) = 10 isn't helpful, so we need a better R
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help-10
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Hyperlix
03/16/2022 10:55:41
yeah I'm figuring out how to find a better R
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help-10
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Shuri2060
03/16/2022 10:55:54
Q(1) = ? Q(2) = ? Q(3) = ? Q(4) = ? First maybe think what we **want** these to be
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help-10
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Shuri2060
03/16/2022 10:56:00
for some useful information
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:56:08
Then you can find a good R
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help-10
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Hyperlix
03/16/2022 10:58:45
ok if I said we want those to be 0, how would it help?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:59:38
If you know Q(1) = 0
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 10:59:43
What does this tell you about Q?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
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Shuri2060
03/16/2022 11:00:22
Is there a theorem you can use perhaps?
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help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:00:35
no idea
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:01:00
(x - 1)
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:01:04
oh
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:01:18
1 is a zero of the function?
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:01:23
well yes
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:01:35
so the theorem you can use is?
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:02:00
no idea
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:02:11
Factor theorem
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:02:17
Remainder theorem
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:02:22
surely you have done either?
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:02:31
maybe
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:02:39
Review it then
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:02:47
otherwise you'll be stuck
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:02:47
I don't know what they are called here
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:03:10
For a polynomial f f(a) = 0 <=> (x-a) is a factor of f(x)
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:04:08
For a polynomial f f(a) = k <=> f(x) = (x-a)g(x) + k for some g
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:04:16
Factor and remainder theorems
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:04:56
yeah I've seen them but I don't understand them enough
1
0
321,445,119,171,756,000
Shuri2060
9525
a μ-er
false
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:05:34
if you can divide a polynomial by (x-a) and the result is 0, then (x-a) is a factor right?
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:05:52
no...
0
1
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:06:06
what
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
898,441,976,142,237,800
Hyperlix
03/16/2022 11:06:09
why
1
0
null
null
null
null
null
1,278
help-10
a446f8916c9c48a499caa8c8f0fa7a7f
321,445,119,171,756,000
Shuri2060
03/16/2022 11:06:21
if i divide a polynomial by another polynomial I won't get 0
0
1
null
null
null
null
null