The problem asks us to factor the quadratic expression $6a^2 - 18a - 60$ completely, if possible. If the polynomial is prime, we should choose option B.

1. Problem Description

The problem asks us to factor the quadratic expression $6a^2 - 18a - 60$ completely, if possible. If the polynomial is prime, we should choose option B.

2. Solution Steps

First, we check for a common factor among the coefficients. The coefficients are $6$, $-18$, and $-60$. The greatest common divisor of these numbers is $6$. We factor out the $6$ to get

$6a^2 - 18a - 60 = 6(a^2 - 3a - 10)$.

Now, we want to factor the quadratic expression $a^2 - 3a - 10$. We are looking for two numbers that multiply to $-10$ and add to $-3$. These two numbers are $-5$ and $2$. Therefore, $a^2 - 3a - 10 = (a - 5)(a + 2)$.

Thus, $6a^2 - 18a - 60 = 6(a - 5)(a + 2)$.

3. Final Answer

The factored form of $6a^2 - 18a - 60$ is $6(a - 5)(a + 2)$.

Final Answer: $6(a - 5)(a + 2)$