Factoring a quadratic
Find two numbers that multiply to the last term and add to the middle one.
A worked example
Factor x^2 + 7x + 12. Two numbers multiplying to 12 and adding to 7 are 3 and 4, so it factors to (x + 3)(x + 4).
The mistake people actually make
Check the signs. For x^2 - 7x + 12 both numbers are negative: (x - 3)(x - 4).