Question

factor each expression
9w² - 75w - 54

Explanation:

Step1: Factor out GCF

First, find the greatest common factor (GCF) of $9w^2$, $-75w$, and $-54$. The GCF is 3.
$9w^2 -75w -54 = 3(3w^2 -25w -18)$

Step2: Factor quadratic trinomial

Factor $3w^2 -25w -18$ by finding two numbers that multiply to $3\times(-18)=-54$ and add to $-25$. These numbers are $-27$ and $2$. Split the middle term and factor by grouping:
$3w^2 -27w +2w -18 = 3w(w-9) +2(w-9) = (3w+2)(w-9)$

Step3: Combine factors

Substitute the factored quadratic back into the expression from Step1.
$3(3w+2)(w-9)$

Answer:

$3(3w+2)(w-9)$