Topic: Factoring

Subtopic: Trinomials

**Overview**

Remember "prime factoring" from an arithmetic class, e.g. 12=2*2*3? Well, that is what we are going to do in this lesson, except with polynomials. Factoring a polynomial is basically "unFOILing", so we will basically be doing FOIL backwards. Instead of starting with (x-2)(x+5) and FOILing to get the polynomial, we will start with x^{2}+3x-10 and factor down to the two binomials. So FOILing goes from (x-2)(x+5) to x^{2}+3x-10 and FACTORING goes from x^{2}+3x-10 to (x-2)(x+5).

There are two main methods to factoring a trinomial, the trial-and-check method and the ab-method. Both methods work on any factorable trinomial, so use the one that make the most sense to you. In this lesson we will factor trinomials of the form 1x^{2}+bx+c and of the form ax^{2}+bx+c where the coefficient of the x isn't 1. The latter is much trickier and will take some practice! Look for patterns with the signs to ease the process of factoring down. Be sure your final answer is completely factored.

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 7.2.1 Factor trinomials down into a product of binomials
- 7.2.2 Recognize "prime" trinomials
- 7.2.3 Factor the GCF from a trinomial and the resulting trinomial down into a product of binomials so that the final answer is of the form coefficient(binomial)(binomial)

**Terminology**

Define: prime polynomial, product of binomials