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!
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
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 6.2-6.3
- ch 6.2 covers factoring trinomials of the form 1x2+bx+c. Practice lots of these before moving to the trickier ...
- ch 6.3 covers factoring trinomials of the form ax2+bx+c. When factoring these expressions, look for patterns with the signs to ease the process of factoring down. Be sure your final answer is completely factored.