Solve The form x² - bx - c in  Factoring Polynomials ?

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

x² - 11x - 12

(No lead coefficient; negative 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 negative, you should always make the larger factor negative:

-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 negative. (Because of the negative coefficient -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.

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.