Question

factor completely: $x^2 - 17x + 72$
$x(x - 3)$
$(x - 9)(x + 8)$
$(x - 9)(x - 8)$
$(x + 9)(x + 8)$

Explanation:

Step1: Find pair summing to -17

We need two numbers that multiply to $72$ and add to $-17$. These numbers are $-9$ and $-8$, since $(-9)\times(-8)=72$ and $(-9)+(-8)=-17$.

Step2: Factor the quadratic

Rewrite the quadratic using the pair, then factor by grouping:
$$x^2 -17x +72 = x^2 -9x -8x +72 = x(x-9)-8(x-9)=(x-9)(x-8)$$

Answer:

$(x - 9)(x - 8)$