Question

For what value of m, p(x) = (x³ − 2mx² + 16) is divisible by (x + 2)?

Answer 1

$$\begin{gathered} \mathrm{Let}: \\ p\left(x\right)=x^3-2m{x}^2+16 \end{gathered}$$
Now, we have:
$x+2=0\Rightarrow x=-2$
$$\begin{gathered} p\left(x\right)\text{is divisible by}\left(x+2\right). \\ \Rightarrow p\left(-2\right)=0 \\ \Rightarrow {\left(-2\right)}^3-2m{\left(-2\right)}^2+16=0 \\ \Rightarrow -8-8m+16=0 \\ \Rightarrow 8-8m=0 \\ \Rightarrow m=\frac{8}{8} \\ \Rightarrow m=1 \end{gathered}$$

Hence, the value of m is 1.