You may want to review factoring out GCDs first.
Sometimes, there's nothing obvious to factor out of a whole polynomial, but you can still factor something out of some of the terms. For example, suppose you have 4xy + 4x + y + 1. There's nothing that goes into all four terms, but the GCD of the first two terms is 4x. So we can factor it out, getting 4x(y + 1) + y + 1. (In general, we could try to factor something out of the last two terms, too, but in this case nothing works.)
What's the point of this? Well, not much in general, but, in this case (and generally on this section of the website), note that the first part of the expression is something times y + 1, and what's left is also something (in this case 1) times y + 1. So now the GCD of the two parts is y + 1, and the whole thing can be rewritten as (4x + 1)(y + 1), which is a factorization.