Question

factor completely. 3w^2 - 51w + 90

Explanation:

Step1: Factor out GCF

First, find the greatest - common factor of the coefficients 3, - 51, and 90. The GCF of 3, - 51, and 90 is 3.
$3w^{2}-51w + 90=3(w^{2}-17w + 30)$

Step2: Factor the quadratic trinomial

For the quadratic trinomial $w^{2}-17w + 30$, we need to find two numbers that multiply to 30 and add up to - 17. The numbers are - 15 and - 2 since $(-15)\times(-2)=30$ and $-15+( - 2)=-17$.
$w^{2}-17w + 30=(w - 15)(w - 2)$

Answer:

$3(w - 15)(w - 2)$