Question

factor completely. 3g^2 - 36g + 33

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of the coefficients 3, - 36, and 33. The GCF of 3, - 36, and 33 is 3. So we can write:
$3g^{2}-36g + 33=3(g^{2}-12g + 11)$

Step2: Factor the quadratic trinomial

For the quadratic trinomial $g^{2}-12g + 11$, we need to find two numbers that multiply to 11 and add up to - 12. The numbers are - 11 and - 1. So we can factor it as:
$g^{2}-12g + 11=(g - 11)(g - 1)$

Answer:

$3(g - 11)(g - 1)$