The problem asks to factor the polynomial $4x^3 + 14x^2 - 30x$ by first factoring out the greatest common factor (GCF).

1. Problem Description

The problem asks to factor the polynomial $4x^3 + 14x^2 - 30x$ by first factoring out the greatest common factor (GCF).

2. Solution Steps

First, we identify the coefficients: 4, 14, and -

3

0. We find the GCF of these coefficients.

The factors of 4 are 1, 2, and

4. The factors of 14 are 1, 2, 7, and

1

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

3

0. The GCF of 4, 14, and 30 is

2.

Next, we identify the variable terms: $x^3$, $x^2$, and $x$. The GCF of these variable terms is $x$.

Therefore, the greatest common factor of the polynomial $4x^3 + 14x^2 - 30x$ is $2x$.

Now, we factor out $2x$ from each term of the polynomial:

$4x^3 + 14x^2 - 30x = 2x(2x^2 + 7x - 15)$.

3. Final Answer

$2x(2x^2 + 7x - 15)$