Factoring quadratics of the form x² + bx + c ?

This tutorial will help you factor quadratics that look something like this:
x² + 7x + 12

(Positive coefficients; no leading coefficient.)

Step 1: Write down all the different ways to factor the constant coefficient (12) into two whole numbers:
12 = 1 * 12
12 = 2 * 6
12 = 3 * 4
(Order doesn't matter. So 3 * 4 is the same as 4 * 3.)

Step 2: Now, for each possible factorization, add together the two factors. You're looking for two that add up to the middle coefficient, which is 7.

1 + 12 = 13
2 + 6 = 8
3 + 4 = 7 < --------------------------- found it!
The factors which worked out were 3 and 4, so here's how you factor the polynomial:
(x + 3)(x + 4)

Step 3: Check your answer by multiplying out using FOIL:
(x + 3)(x + 4) = x² + 7x + 12.