1. Polynomials and Polynomial Functions
*Chapter 5
Polynomials and Polynomial Functions

2. Chapter Sections 5.1 – Addition and Subtraction of Polynomials
5.2 – Multiplication of Polynomials
5.3 – Division of Polynomials and Synthetic Division
5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping
5.5 – Factoring Trinomials
5.6 – Special Factoring Formulas
5.7-A General Review of Factoring
5.8- Polynomial Equations
Chapter 1 Outline

3. Recall: Special Products:
(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2
(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2

4. Factoring a Monomial from a Polynomial and Factoring by Grouping
§ 5.4
Factoring a Monomial from a Polynomial and Factoring by Grouping
Objectives:
1. Find the greatest common factor of a set of numbers or monomials.
2. Write a polynomial as a product of a monomial GCF and a polynomial.
3. Factor by grouping.

5. Recall: Determining the GCF
Example: 45a3b and 30a2
Solution:
45a3b = 32 • 5 • a3 • b
30a2 = 2 • 3 • 5 • a2
Example: Find the GCF of 3240 and 8316.
Solution:
Write the prime factorization of each number.
3240 = 23 • 34 • 5
8316 = 22 • 33 • 7 • 11
GCF = 22 • 33 = 108
LCM = • 5 • 7 • 11 =
Factored form:
A number or an expression written as a product of factors.
If a · b = c, then a and b are of c.
a·b
factors
GCF = 3 • 5 • a2 = 15a2

6. Factoring a Monomial from a Polynomial
Find the GCF
Each term = the GCF × some factor
Use the distributive property to factor out the GCF.
Example1: 15x4 – 5x3+25x2
(GCF is 5x2)

7. Example 2: Factor:

8. Factoring by Grouping Example 3: : a) Factor x2 + 7x + 3x + 21.
Fid GCF for all
Factor the GCF from each
Get 2 groups of 2 terms such that each group has the same Binomial GCF.
Factor out the Binomial GCF
Factoring by Grouping
Factoring a polynomial of 4 or more terms by taking common
factors from groups of terms is called factoring by grouping.
Example 3: : a) Factor x2 + 7x + 3x + 21.
x(x + 7) + 3(x + 7) =
(x + 7) (x + 3)

9. Example 4: Factor.