Question

If the expression $(p{x}^3+x^2-2x-q)$ is divisible by $(x-1)$ and $(x+1)$, what are the values of $p$ and $q$ respectively?

• A. $2,-1$
• B. $-2,1$
• C. $-2,-1$
• D. $2,1$

Answer 1

Answer: (D)

$2,1$

Let $f\left(x\right)=p{x}^3+x^2-2x-q$
Since $f\left(x\right)$ is divisible by $(x-1)$ and $(x+1)$ so $x=1$ and $-1$ must make $f\left(x\right)=0$.
Therefore, $p+1-2-q=0$, i.e., $p-q=1$; and
$-p+1+2-q=0$, i.e., $p+q=3$
Thus $p=2$ and $q=1$