Question

factor completely. 4y^{2}-28y - 32

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of 4, 28, and 32. The GCF of 4, 28, and 32 is 4.
$4y^{2}-28y - 32=4(y^{2}-7y - 8)$

Step2: Factor the quadratic trinomial

For the quadratic trinomial $y^{2}-7y - 8$, we need to find two numbers that multiply to - 8 and add up to - 7. The numbers are - 8 and 1.
$y^{2}-7y - 8=y^{2}-8y + y-8=y(y - 8)+1(y - 8)=(y - 8)(y + 1)$

Answer:

$4(y - 8)(y + 1)$