The problem asks us to factor the polynomial $5x^2 - 10x - xy + 2y$, if possible. If the polynomial cannot be factored, we must identify it as prime.

1. Problem Description

The problem asks us to factor the polynomial $5x^2 - 10x - xy + 2y$, if possible. If the polynomial cannot be factored, we must identify it as prime.

2. Solution Steps

We can attempt to factor the polynomial $5x^2 - 10x - xy + 2y$ by grouping. We group the first two terms and the last two terms:

$(5x^2 - 10x) + (-xy + 2y)$.

We can factor out $5x$ from the first group and $-y$ from the second group:

$5x(x - 2) - y(x - 2)$.

Now, we can factor out $(x - 2)$ from both terms:

$(x - 2)(5x - y)$.

Therefore, the factored form of the polynomial $5x^2 - 10x - xy + 2y$ is $(x - 2)(5x - y)$.

3. Final Answer

$5x^2 - 10x - xy + 2y = (x - 2)(5x - y)$

Final Answer: A. $(x - 2)(5x - y)$