Question

factor completely. 3f^2 - 6f - 45

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of the coefficients 3, - 6, and - 45. The GCF of 3, - 6, and - 45 is 3.
$3f^{2}-6f - 45=3(f^{2}-2f - 15)$

Step2: Factor the quadratic expression

For the quadratic expression $f^{2}-2f - 15$, we need to find two numbers that multiply to - 15 and add up to - 2. The numbers are - 5 and 3.
$f^{2}-2f - 15=(f - 5)(f+3)$

Answer:

$3(f - 5)(f + 3)$