Question

If $f\left(x\right)=-2(x^2-6x-12)+3(p-x)$ and $f\left(x\right)$ is evenly divisible by $x$, then what is the value of $p$?

• A. -8
• B. -3
• C. 2
• D. 3

Answer 1

Answer: (A)

-8

Applying remainder theorem,
$f\left(x\right)$ is evenly divisible by $x$, that is $x=0$
Apply $x=0$ in the equation $f\left(x\right)=-2(x^2-6x-12)+3(p-x)$
$f\left(x\right)=-2(0^2-6(0)-12)+3(p-(0\left)\right)$
$\Rightarrow 24+3p=0$
$\Rightarrow 24=-3p$
$\Rightarrow p=-8$