The problem asks to factor the polynomial $5x^2 + 5x - 60$. First, factor out the greatest common factor (GCF) from each term, and then factor the remaining polynomial.

1. Problem Description

The problem asks to factor the polynomial $5x^2 + 5x - 60$. First, factor out the greatest common factor (GCF) from each term, and then factor the remaining polynomial.

2. Solution Steps

First, we find the greatest common factor (GCF) of the coefficients $5, 5,$ and $-60$. The GCF is $5$.

Factoring out the GCF, we have:

$5x^2 + 5x - 60 = 5(x^2 + x - 12)$

Now, we need to factor the quadratic expression $x^2 + x - 12$. We are looking for two numbers that multiply to $-12$ and add to $1$. These numbers are $4$ and $-3$.

Therefore, we can factor the quadratic as:

$x^2 + x - 12 = (x + 4)(x - 3)$

Combining this with the GCF we factored out earlier, we have:

$5x^2 + 5x - 60 = 5(x + 4)(x - 3)$

3. Final Answer

$5(x+4)(x-3)$