The form x2 - bx + c ?

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

x² -7x + 12

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

Step 1: Write down all the different ways to factor the constant coefficient (12) into two negative 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.