Question

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

Answer 1

According to factor theorm

$x-2$ is factor of $x^3-4x^2-4$ only if $x=2$ is zero of polynomial

so at $x=2$$x^3-4x^2-4$

$=2^3-{42}^2-4$

$=8-16-4=-12\ne 0$

So $x-2$ is not factor of the polynomial