CHAPTER 5
Factoring Polynomials
Source:
Elementary & Intermediate Algebra, Fourth Edition
Prepared and Edited by:
Dr. Mohamad Hammoudi

Topics of Chapter 5
5.1: An Introduction to Factoring.
5.2: Factoring Special Polynomials.
5.3: Factoring Trinomials: Trial and Error.
5.4: Factoring Trinomials: The
ac
Method.
5.5: Strategies in Factoring.
5.6: Solving Quadratic Equations by Factoring.
5.7: Problem Solving with Factoring.
2

5.1: Introduction to Factoring
Objectives:
5.1.1: Factor out the greatest common factor (GCF)
5.1.2: Factor by grouping
3

5.1: Introduction to Factoring
In Chapter 4 you were given factors and asked to find a
product.
In Chapter 5, we will reverse the process.
You will be given a polynomial and asked to find its factors.
This is called
factoring
.
Examples from arithmetic:
To multiply 5 . 7, we write 5 . 7 = 35
To factor 35, we write 35 = 5 . 7
Examples from algebra:
To multiply a(b + c), we write a(b + c) = ab + ac
To factor ab + ac = a(b + c)
To multiply 3(x + 5), we write 3(x + 5) = 3x + 15
To factor 3x + 15, we write 3x + 15 = 3(x + 5)
4

5.1.1: Factor out the Greatest Common Factor (GCF)
To factor 3x + 15, we write 3x + 15 = 3(x + 5)
The original terms are each divided by the
greatest common
factor
to determine the expression in parentheses.
The first step in factoring is to identify the
greatest common
factor (GCF)
of a set of terms.
5

5.1.1: Factor out the Greatest Common Factor (GCF)
Examples:
Find the GCF for each list of terms.
1.
9 and 12
2.
10, 25, 150
3.
x
4
and x
7
4.
12a
3
and 18a
2
To Factor a Monomial from a Polynomial
6

5.1.1: Factor out the Greatest Common Factor (GCF)
Examples:
Factor the followings.
1.
12x
2
+ 12x
2.
6a
4
–
18a
2
3.
5x
2
–
10x + 15
4.
6ab + 9ab
2
–
15a
2
5.
4a
4
+ 12a
3
–
20a
2
6.
6a
2
b + 9ab
2
+ 3ab
7

5.1.2: Factor by Grouping
If the terms of a polynomial have no common factor (other
than 1), factoring by grouping is the preferred method.

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