Factoring Trinomials of the Type ax ² + bx + c

There are two methods.

• Factoring with FOIL (AKA Guess-and-check).

Examples:

1. 3x ² - 14x - 5

Note that there are four possibilities. And it’s rather time consuming to have to FOIL each time to find out if you have the right answer or not.

2. 4x ² + 13x - 12

• This one’s a real pain since there are, in fact, 12 possibilities.

The Grouping Method (AKA The ac-method).

Example:

4x ² + 13x - 12

There’s still an aspect of guess-and-check here, but it involves integers rather than binomials and the check is simply addition. I find it much easier, myself.