LESSON NOTES MENU
Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Intermediate Algebra
Topic: Factoring
Subtopic: GCFs & Grouping

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 "unmultiplying". Whereas distributing takes 7x(2x+3) to 14x2+21x, factoring does this backwards taking 14x2+21x to 7x(2x+3). There are several methods of factoring, but we will start with the GCF method and the grouping method. Two things to keep in mind:

• Always factor the GCF out first - no matter what other methods of factoring might be involved, start with the GCF.
• Grouping method only works when the poly has an even number of terms (usually 4).
• Caution: Expressions can only factored and not solved. The original problem must contain an equals sign (thus be an equation) to be able to be solved for x. This is a very important difference!
Factoring is used extensively in the remainder of the course so really spend some quality time this week practicing problems. As you do so look for patterns that may help you to identify which factoring method works on which polynomials.

Objectives

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

• 7.1.1 Recognize the GCF of two (or more) monomials
• 7.1.2 Factor a polynomial by pulling out the GCF
• 7.1.3 Accurately factor out a GCF that is negative
• 7.1.4 Factor a polynomial by the grouping method
• 7.1.5 Recognize when a polynomial is completely factored

Terminology

Terms you should be able to define: to factor, a factor, factored form, "completely factored form", product, "a product of factors", GCF = greatest common factor, grouping method, "to group factor"