Question

Using factor theorem show $x-2$ is a factor of $x^6-64$

Answer 1

Let $f\left(x\right)=x^6-64$

By factor theorem, $x-R$ is a factor of $f\left(x\right)$ if and only if $f\left(R\right)=0$, here, $R=2$ and $f\left(x\right)=f\left(2\right)=2^6-64=-64=0$

$\Rightarrow (x-2)$ is a factor of $x^6-64$