Question

what is x cubed minus 8

Answer 1

Since $x^3-8$ is a sum of cubes, (-8 is -2 cubed) it can be factored like so:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

$a^3=x^3\implies a=x$
$b^3=-8\implies b=-2$

$x^3-8=(x+(-2))(x^2-x(-2)+(-2)^2)=\boxed{(x-2)(x^2+2x+4)}$