Question

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Explanation:

Step1: Identify GCF of terms

The terms are $-3z$ and $-12$. The greatest common factor is $-3$.

Step2: Factor out the GCF

Divide each term by $-3$:
$\frac{-3z}{-3} = z$, $\frac{-12}{-3} = 4$
Rewrite the expression: $-3(z + 4)$

Step3: Address the final fraction

The given fraction is $\frac{-4(z+4)}{?}$. Since the original factored expression is $-3(z+4) = -3z -12$, to relate it, if we assume the denominator is the GCF we found, but correcting the fraction context: the factored form of the original expression is $-3(z+4)$, so if we have $\frac{-4(z+4)}{x} = -3z -12$, solve for $x$:
$x = \frac{-4(z+4)}{-3(z+4)} = \frac{4}{3}$ (canceling $z+4$ for $z
eq -4$)

Answer:

Greatest Common Factor: $-3$
Factored Expression: $-3(z + 4)$
Denominator for the fraction: $\frac{4}{3}$