Question

For what value of m is $x^2-2m{x}^2+16$ divisible by $x+2$?

Answer 1

From Remainder theorem, we have

$f\left(x\right)$ is divisible by $(x-a)$ iff

$f\left(a\right)=0$

$\therefore f\left(x\right)=x^2-2m{x}^2+16$ is divisible by $x+2$

if $f(-2)=0$

$\Rightarrow (-2{)}^2-2m(-2{)}^2+16=0$

$\Rightarrow 4-2m\left(4\right)+16=0$

$\Rightarrow 20=2m\left(4\right)$

$\Rightarrow m=\frac{20}{8}=\frac{5}{2}=2.5$

$\therefore m=2.5$