Question

If $(x+2)$ is a factor of $2x^3+5x^2-x-k$, then value of k is :

• A. 6
• B. -24
• C. -6
• D. 24

Answer 1

The correct option is A 6

$p\left(x\right)=2x^3+5x^2-x-k$

Since $x+2$ is a factor of $p\left(x\right)$,

For $x+2=0$, i.e; $x=-2$, $p\left(x\right)=0$

So, $p(-2)=2(-2{)}^3+5(-2{)}^2-(-2)-k$

$\Rightarrow -16+20+2-k=0$

$\Rightarrow k=6$