Question

The value of $m$ for which $x^3-2m{x}^2+16$ is divisible by $(x+2)$, is

• A. $1$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

The correct option is A $1$

Let $p\left(x\right)=x^3-2m{x}^2+16$ and $g\left(x\right)=x+2$
Now, $g\left(x\right)=x+2$
$x+2=0$
$x=-2$
If $p\left(x\right)$ is divisible $g\left(x\right)$, then $p(-2)$ must be $0$.
Thus, $p(-2)=0$
$\Rightarrow (-2{)}^3-2m(-2{)}^2+16=0$
$\Rightarrow -8-8m+16=0$
$\Rightarrow -8m=-8$
$\Rightarrow m=1$