Question

factor completely. 2q^{2}+2q - 4

Explanation:

Step1: Factor out the GCF

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

Step2: Factor the quadratic expression

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

Answer:

$2(q + 2)(q - 1)$