The problem is to factor the expression $9x^3 + 30x^2 - 24x$ by first factoring out the greatest common factor (GCF).

1. Problem Description

The problem is to factor the expression $9x^3 + 30x^2 - 24x$ by first factoring out the greatest common factor (GCF).

2. Solution Steps

First, we identify the greatest common factor of the coefficients 9, 30, and -

2

4. The factors of 9 are 1, 3, and

9. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and

3

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

2

4. The greatest common factor of the coefficients is

3.

Next, we identify the greatest common factor of the variable terms $x^3$, $x^2$, and $x$. The GCF is $x$.

Therefore, the greatest common factor of the entire expression is $3x$.

Now, we factor out $3x$ from each term:

$9x^3 + 30x^2 - 24x = 3x(3x^2 + 10x - 8)$

3. Final Answer

$3x^2 + 10x - 8$