The problem asks to factor out the greatest common factor (GCF) from the polynomial $12z^2 - 48z$.

1. Problem Description

The problem asks to factor out the greatest common factor (GCF) from the polynomial $12z^2 - 48z$.

2. Solution Steps

First, we identify the greatest common factor of the coefficients 12 and

4

8. The factors of 12 are 1, 2, 3, 4, 6, and

1

2. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and

4

8. The greatest common factor of 12 and 48 is

1

2.

Next, we identify the greatest common factor of the variable terms $z^2$ and $z$.

Since $z^2 = z \cdot z$ and $z = z$, the greatest common factor of $z^2$ and $z$ is $z$.

Therefore, the greatest common factor of $12z^2$ and $48z$ is $12z$.

Now we factor out $12z$ from the given polynomial:

$12z^2 - 48z = 12z(z) - 12z(4) = 12z(z - 4)$.

3. Final Answer

$12z(z-4)$