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Calculus III

Course: Intermediate Algebra
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 x2+3x-10 and factor down to the two binomials. So FOILing goes from (x-2)(x+5) to x2+3x-10 and FACTORING goes from x2+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 1x2+bx+c and of the form ax2+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

Terms you should be able to define: prime polynomial, product of binomials