Question

factor: $x^2 - 9x + 20$
$(x - 5)(x - 4)$
$(x - 5)(x + 4)$
$(x - 10)(x - 2)$
$(x + $

Explanation:

Step1: Find pair summing to -9, product 20

We need two numbers that add to $-9$ and multiply to $20$. These numbers are $-4$ and $-5$.

Step2: Write factored form

Substitute the pair into binomial factors.
$x^2 -9x +20=(x-4)(x-5)$

Step3: Verify the factors

Expand $(x-5)(x-4)$:
$$(x-5)(x-4)=x^2 -4x -5x +20=x^2 -9x +20$$

Answer:

$\boldsymbol{(x - 5)(x - 4)}$