Question

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

Explanation:

Step1: Identify target sum and product

We need two numbers that add to $-17$ and multiply to $72$.

Step2: Find the pair of numbers

The numbers $-9$ and $-8$ satisfy: $-9 + (-8) = -17$ and $(-9)\times(-8)=72$.

Step3: Write the factored form

Substitute the numbers into the binomial factors.

Answer:

C. $(x-9)(x-8)$