Question

choose the values of a and b that represent the factored form of $w^2 - 11w + 18$.
$w^2 - 11w + 18 = (w - a)(w - b)$
a = 2 $checkmark$
b = 9 $checkmark$

Explanation:

Step1: Find pair summing to -11, product 18

We need two numbers that add to $-11$ and multiply to $18$. These numbers are $-2$ and $-9$.

Step2: Rewrite quadratic in factored form

$w^2 -11w +18=(w-2)(w-9)$

Step3: Match to given form $(w-a)(w-b)$

Compare $(w-2)(w-9)$ to $(w-a)(w-b)$, so $a=2$, $b=9$.

Answer:

$a=2$, $b=9$