Question

factor completely.
4n² + 4n - 24

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of the coefficients 4, 4, and 24. The GCF of 4, 4, and 24 is 4.
$4n^{2}+4n - 24=4(n^{2}+n - 6)$

Step2: Factor the quadratic expression

Factor the quadratic $n^{2}+n - 6$. We need to find two numbers that multiply to - 6 and add up to 1. The numbers are 3 and - 2.
$n^{2}+n - 6=(n + 3)(n - 2)$

Answer:

$4(n + 3)(n - 2)$