You may want to review GCDs and factoring without them first.

Sometimes, a polynomial has a GCD, and *then* you still
can factor it some other way. For example, suppose you're given
2*x*^{2} − 12*x* + 10. This has a GCD of
2, which you can factor out, getting 2(*x*^{2}
− 6*x* + 5). But now you can factor the polynomial in
parentheses the way we already know, so the final answer is
2(*x* − 1)(*x* − 5).