Answer
$(x+2)(x-4)$
Work Step by Step
To factor a second-degree polynomial $x^2 -2x - 8$, we have to find integers whose product is $-8$ and whose sum is $-2$. That is, we have $2$ and $-4$ where $2-4=-2$ and $2\times (-4)=-8$. Thus:
$$
x^2 - 2x - 8=(x+2)(x-4)
.$$