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 2x2 − 12x + 10. This has a GCD of 2, which you can factor out, getting 2(x2 − 6x + 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).