Question

Divide using factor theorem, whether $(x-2)$ is a factor of $x^3-4x^2-4.$

Answer 1

$x-2=0$

$x=2$

Now

$p\left(x\right)=x^3-4x^2-4$

$p\left(2\right)=2^3-4(2{)}^2-4$

$=8-4\left(4\right)-4$

$=8-16-4$

$=8-20$

$=-12\ne 0$

$\therefore x-2$ is not a factor