Answer
$(x+1)(x-8)$
Work Step by Step
To factor a second-degree polynomial $x^2 -7x - 8$, we have to find integers whose product is $-8$ and whose sum is $-7$. That is, we have $1$ and $-8$ where $1-8=-7$ and $1\times (-8)=-8$. Thus:
$$
x^2 - 7x - 8=(x+1)(x-8)
.$$