Question

factor completely.
4z^{2}+44z + 96
4(z + 11)(z

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of the coefficients 4, 44, and 96. The GCF of 4, 44, and 96 is 4.
$4z^{2}+44z + 96=4(z^{2}+11z + 24)$

Step2: Factor the quadratic trinomial

For the quadratic trinomial $z^{2}+11z + 24$, we need to find two numbers that multiply to 24 and add up to 11. The numbers are 3 and 8 since $3\times8 = 24$ and $3 + 8=11$.
$z^{2}+11z + 24=(z + 3)(z + 8)$

Answer:

$4(z + 3)(z + 8)$