$Algebra problem$

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$Algebra problem$

When the polynomial $2x^2+bx-6$ is divided by $x+1$, the remainder is $-2$. What is the remainder when the polynomial is divided by $x-1$?

A. -8
B. -5
C. -6
D. 9

Algebra Precalculus

Arnomk

44

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We have
\[2x^2+bx-6=(x+1)(ax+c)-2,\]
where $a, c$ are two constants. Substituting $x$ with $-1$ we get
\[2(-1)^2+b(-1)-6=-2 \Rightarrow -b-4=-2 \Rightarrow b=-2.\]
On the other hand
\[ (1) 2x^2-2x-6=(x-1)(ax+c)+R,\]
where $R$ is the remainder of $2x^2-2x-6$ when divided by $(x-1)$. Substituting $x$ by $1$ in equation (1) we get
\[2(1)^2-2-6=R \Rightarrow R=-6.\]
So the correct answer is C.

Nicolasp

163

$Algebra problem$

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