Solve the form x² + bx - c ?

This tutorial will help you factor quadratics that look something like this:

x² + 11x - 12

(No lead coefficient; positive middle coefficient; negative constant coefficient.)

Step 1: Write down all the different ways to factor the constant coefficient (-12) into one negative factor and one positive. (Hint: since the middle coefficient, 11, is a positive, you should always make the larger factor positive:

-12 = ( -1)(+12 )
-12 = ( -2)( +6 )
-12 = ( -3)( +4 )

Remember, don't bother writing down (-4)(+3), because you want the larger number to be positive. (Because of the positive 11 in the original polynomial.)

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 +11.

-1 + 12 = 11 < ------------------- found it!
The factors which worked out were -1 and 12, so here's how you factor the polynomial:

(x - 1)(x + 12)

Step 3: Check your answer by multiplying out using FOIL:

(x - 1)(x + 12) = x² + 11x - 12.