Question

factor $5z^2 + 45z$. the factored polynomial is \boxed{}.

Explanation:

Step1: Identify greatest common factor

The terms are $5z^2$ and $45z$. The greatest common factor (GCF) of 5 and 45 is 5, and the GCF of $z^2$ and $z$ is $z$. So overall GCF is $5z$.

Step2: Factor out the GCF

Divide each term by $5z$: $\frac{5z^2}{5z} = z$, $\frac{45z}{5z} = 9$. Write as product of GCF and remaining terms.
$5z(z + 9)$

Answer:

$5z(z + 9)$