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Can /sci/ do basic algebra?

Anonymous Mon 01 Feb 23:19:40 2021 No.12654267 View Reply Original Report

Quoted By: >>12654293 >>12654393

For a polynomial p(x), the value of p(3) is -2. Which of the following must be true about p(x)?
A) (x-5) is a factor of p(x),
B) (x-2) is a factor of p(x),
C) (x+2) is a factor of p(x),
D) The remainder when p(x) is divided by (x-3) is -2.

Anonymous

Anonymous Mon 01 Feb 2021 23:26:11 No.12654293 Report

Quoted By:

>>12654267
>A) (x-5) is a factor of p(x),
>B) (x-2) is a factor of p(x),
>C) (x+2) is a factor of p(x),
Obviously no
>D) The remainder when p(x) is divided by (x-3) is -2.
??? Let q(x)=p(x)+2 then (x-3) | q(x) so (x-3) | p(x)-2. Ok true, never thought about that.

Anonymous

Anonymous Mon 01 Feb 2021 23:29:03 No.12654304 Report

Quoted By: >>12654317

it's D, assuming that one of them is true, you can show counter examples for A-C:
A: p(x) = $p(x)=\left(x-5\right)\left(x-1\right)$
B: p(x) = $p(x)=\left(x-2\right)$
C: p(x) = $p(x)=\left(x+3\right)$
if you don't like this you can look at it differently, if D is true that would mean $p(x)=d(x)\cdot\left(x-3\right)-2$
such that d(x) is any other polynomial, plug in 3 and you get your answer

Anonymous

Anonymous Mon 01 Feb 2021 23:32:28 No.12654317 Report

Quoted By: >>12654377

>>12654304
>it's D, assuming that one of them is true, you can show counter examples for A-C:
p(x)=-2

Anonymous

Anonymous Mon 01 Feb 2021 23:39:11 No.12654349 Report

Quoted By:

first three are obviously wrong.

lets prove D

$\frac{p(x)}{x-3}=q(x) + R(x)$
so that q is an other polynomial and R is a rational function
it's obvious that R(x) is $\frac{r}{x-3}$ such that $r\in \mathbb{R}$
then
$p(x)=q(x)\cdot\left(x-3\right) + r$
plug in 3 and you get that r is -2

Anonymous

Anonymous Mon 01 Feb 2021 23:45:52 No.12654377 Report

Quoted By: >>12654418

>>12654317
old anon here, I don't think that's a counter example for D, that would mean $p(x)=\left(x-3\right)\cdot 0 - 2$
the remainder is still -2.
Still what I did in that "proof" was still wrong.

Anonymous

Anonymous Mon 01 Feb 2021 23:49:14 No.12654393 Report

Quoted By:

>>12654267
go practice questions fag

Anonymous

Anonymous Mon 01 Feb 2021 23:55:32 No.12654418 Report

Quoted By:

>>12654377
No, it's a less try hard counter example for A-C

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