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:
$$
x^2 + 2x - 8=(x-2)(x+4)
.$$