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1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5

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2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-2 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 Sections

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3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-3 § 5.2 Multiplication of Polynomials

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4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-4 Multiply a Monomial by a Polynomial To multiply polynomials, you must remember that each term of one polynomial must be multiplied by each term of the other polynomial. To multiply monomials, we use the product rule for exponents. Product Rule for Exponents

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5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5 Multiply a Monomial by a Polynomial Example:

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6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6 Multiply a Monomial by a Polynomial When multiplying a monomial by a polynomial that contains more than two terms we can use the expanded form of the distributive property. Distributive Property, Expanded Form

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7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7 Multiply a Monomial by a Polynomial Example:

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8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-8 The FOIL Method Consider (a + b)(c + d): FOILFOIL Stands for the first – multiply the first terms together. (a + b) (c + d): product ac F Stands for the outer – multiply the outer terms together. (a + b) (c + d): product ad O Stands for the inner – multiply the inner terms together. (a + b) (c + d): product bc I Stands for the last – multiply the last terms together. L (a + b) (c + d): product bd The product of the two binomials is the sum of these four products: (a + b)(c + d) = ac + ad + bc + bd.

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9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-9 The FOIL Method Using the FOIL method, multiply (7x + 3)(2x + 4). (7x)(2x) = (7x)(2x) (7x + 3)(2x + 4) F F O O + (7x)(4) + (3)(2x) I I + (3)(4) L L 14x 2 + 28x + 6x + 12 = 14x 2 + 28x + 6x + 12 = 14x 2 + 34x + 12

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10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-10 Find the Square of a Binomial Square of Binomials To square a binomial, add the square of the first term, twice the product of the terms and the square of the second term. (a + b) 2 = (a + b)(a + b) = a 2 + 2ab + b 2 –––– (a – b) 2 = (a – b)(a – b) = a 2 – 2ab + b 2 Example: a.)(3x + 7) 2 = 9x 2 + 42x + 49 b.)(4x 2 – 5y) 2 = 16x 4 – 40x 2 y+ 25y 2

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11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-11 Product of the Sum and Difference The Product of the Sum and Difference of Two Terms This special product is also called the difference of two squares formula. (a + b)(a – b) = a 2 – b 2 Example: a.)(2x + 3y) (2x – 3y) = 4x 2 – 9y 2 b.)(3x + 4/5) (3x – 4/5) = 9x 2 – 16/25

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