How do you factor a polynomial?

Using the FOIL method works with some simple polynomials. FOIL stands for First, Outside, Inside, Last.

For example:

x^2-4x+4 factors to
(x-2)(x-2)
Check your work by multiplying them all. x times x is first, x times -2 is outside, -2 times x is inside, and -2 times -2 is last. Add the terms to get x^2-2x-2x+4 or x^2-4x+4

In the blank equation, (x+a)(x+b), we see that for this type of polynomial ax and bx have to add to make the middle term and a and b have to multiply to equal the final term. Just pick numbers which suit these conditions. It's easy with practice. Difficult to show.