Question

factor completely: $x^2 - 7x - 8$
$5(x+4)(x+5)$
$(x+1)(x+8)$
$(x+1)(x-8)$
$(x-1)(x+8)$

Explanation:

Step1: Find pair for -8, sum to -7

We need two numbers that multiply to $-8$ and add to $-7$. These numbers are $1$ and $-8$.

Step2: Split middle term, factor

Rewrite the quadratic and factor by grouping:
$$x^2 + x - 8x - 8 = x(x+1) -8(x+1) = (x+1)(x-8)$$

Answer:

$(x+1)(x-8)$