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Chapter 5 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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Multiplying Polynomials 1 1 3 3 2 2 5.55.5 Multiply a monomial and a polynomial. Multiply two polynomials. Multiply binomials by the FOIL method.

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Multiply a monomial and a polynomial. Slide 5.5 - 3

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To find the product of a monomial and a polynomial with more than one term we use the distributive property and multiplication of monomials. Multiply a monomial and a polynomial. As shown in Section 5.1, we find the product of two monomials by using the rules for exponents and the commutative and associative properties. For example Slide 5.5 - 4 Do not confuse addition of terms with multiplication of terms. For instance,, but

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1 Multiplying Monomials and Polynomials Solution: Slide 5.5 - 5 Find the product.

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Multiply two polynomials. Slide 5.5 - 6

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Multiply two polynomials. We can use the distributive property repeatedly to find the product of any two polynomials. For example, to find the product of the polynomials x 2 + 3x +5 and x − 4, think of x − 4 as a single quantity and use the distributive property as follows. Slide 5.5 - 7 Now use the distributive property three more times to find x 2 (x − 4), 3x(x − 4), and 5(x − 4). This example suggests the following rule. To multiply polynomials, multiply each term of the second polynomial by each term of the first polynomial and add the products.

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 2 Multiplying Two Polynomials Slide 5.5 - 8 Multiply (m 3 − 2m + 1)·(2m 2 + 4m + 3). Solution:

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Multiplying Polynomials Vertically Slide 5.5 - 9 Multiply. Solution:

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Multiplying Polynomials with Fractional Coefficients Vertically Slide 5.5 - 10 Multiply. Solution:

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4A Multiplying Polynomials with a Rectangle Model Slide 5.5 - 11 Use the rectangle method to find the product Solution:

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Multiply binomials by the FOIL method. Slide 5.5 - 12

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Multiply binomials by the FOIL method. Slide 5.5 - 13 In algebra, many times the polynomials to be multiplied are binomials. For these products, the FOIL method reduces the rectangle method to a systematic approach without the rectangle. A summary of the steps in the FOIL method follows. Step 1: Multiply the two First terms of the binomials to get the first term of the answer. Step 2: Find the Outer product and Inner product and add them (when possible) to get the middle term of the answer. Step 3: Multiply the two Last terms of the binomials to get the last term of the answer.

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Using the FOIL Method Slide 5.5 - 14 Find the product by the FOIL method. Solution:

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 6 Using the FOIL Method Slide 5.5 - 15 Multiply Solution:

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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 7 Using the FOIL Method Slide 5.5 - 16 Find each product. Solution:

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