Question

factor the expression completely.
$-4z^2 - 12z - 8$

Explanation:

Step1: Factor out the GCF

Factor out $-4$ from all terms.
$-4z^2 - 12z - 8 = -4(z^2 + 3z + 2)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $2$ and add to $3$, then factor.
$z^2 + 3z + 2 = (z + 1)(z + 2)$

Step3: Combine factors

Substitute the factored trinomial back.
$-4(z^2 + 3z + 2) = -4(z + 1)(z + 2)$

Answer:

$-4(z + 1)(z + 2)$