The problem asks to factor the quadratic expression $2x^2 - x - 15$.

1. Problem Description

The problem asks to factor the quadratic expression $2x^2 - x - 15$.

2. Solution Steps

We need to find two numbers whose product is equal to $2 * (-15) = -30$ and whose sum is equal to $-1$.

The numbers are $-6$ and $5$, since $(-6) * 5 = -30$ and $(-6) + 5 = -1$.

We rewrite the middle term $-x$ as $-6x + 5x$:

$2x^2 - x - 15 = 2x^2 - 6x + 5x - 15$.

Now, we factor by grouping:

$2x^2 - 6x + 5x - 15 = 2x(x - 3) + 5(x - 3)$.

We can now factor out $(x - 3)$ from both terms:

$2x(x - 3) + 5(x - 3) = (2x + 5)(x - 3)$.

3. Final Answer

$(2x + 5)(x - 3)$