The problem is to factor the quadratic expression $5x^2 + 10x - 15$.

1. Problem Description

The problem is to factor the quadratic expression $5x^2 + 10x - 15$.

2. Solution Steps

First, we can factor out the greatest common factor (GCF) from all the terms, which is

5. $5x^2 + 10x - 15 = 5(x^2 + 2x - 3)$

Now we need to factor the quadratic expression $x^2 + 2x - 3$. We are looking for two numbers that multiply to $-3$ and add up to $2$. These numbers are $3$ and $-1$. Therefore, we can write the quadratic expression as:

$x^2 + 2x - 3 = (x+3)(x-1)$

Putting it all together, we have:

$5x^2 + 10x - 15 = 5(x^2 + 2x - 3) = 5(x+3)(x-1)$

3. Final Answer

The factored form of the expression $5x^2 + 10x - 15$ is $5(x+3)(x-1)$.