10.5: Factoring Trinomials (Reverse FOIL)

Integrated Math 2

Remember FOIL?

(x + 2)(x – 7) = x2 – 5x – 14

F O + I L

To Factor Trinomials, we start with the trinomial and try to find the original two binomials.

How to Factor: Factor x2 + 4x – 12

1. Parenthesis with an x in each group:(x )(x )

2. Draw a big X. The third term goes on top the middle # goes on bottom.

3. Think of two #’s that multiply to get the top, but the same #’s add to get the bottom.

4. Hint!!! List the factors of the top #.5. Place the two correct numbers and their signs in

the parenthesis. It doesn’t matter which number goes where!!!

Reverse FOIL

Some people may find this chart helpful, but reverse FOIL is technically trial and error!

Problem Factored answer

ax2 + bx + c (x + )(x + )

ax2 - bx + c (x - )(x - )

ax2 + bx – c (x + )(x - )

ax2 - bx – c (x + )(x - )

Try These:

1. x2 + 5x + 6

( )( )x x3 2+ +