Polynomials and Polynomial Functions *Chapter 5 Polynomials and Polynomial Functions

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

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

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.

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 = 23 34 • 5 • 7 • 11 = 249480 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

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)

Example 2: Factor:

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)

Example 4: Factor.