1. Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 4 Polynomials

2. 1-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Multiplication of Polynomials Multiplying Monomials Multiplying a Monomial and a Polynomial Multiplying Any Two Polynomials 4.5

3. Copyright © 2014, 2010, and 2006 Pearson Education, Inc. To Multiply Monomials To find an equivalent expression for the product of two monomials, multiply the coefficients and then multiply the variables using the product rule for exponents.

4. 1-4 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply: a) (6x)(7x) b) (5a)(  a) c) (  8x 6 )(3x 4 ) Solution a) (6x)(7x) = (6  7) (x  x) = 42x 2 b) (5a)(  a) = (5a)(  1a) = (5)(  1)(a  a) =  5a 2 c) (  8x 6 )(3x 4 ) = (  8  3) (x 6  x 4 ) =  24x 6 + 4 =  24x 10

5. 1-5 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply: a) x and x + 7 b) 6x(x 2  4x + 5) Solution a) x(x + 7) = x 2 + 7x b) 6x(x 2  4x + 5) = 6x 3  24x 2 + 30x = x  x + x  7 = (6x)(x 2 )  (6x)(4x) + (6x)(5)

6. Copyright © 2014, 2010, and 2006 Pearson Education, Inc. The Product of a Monomial and a Polynomial To multiply a monomial and a polynomial, multiply each term of the polynomial by the monomial.

7. 1-7 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply: 5x 2 (x 3  4x 2 + 3x  5) Solution 5x 2 (x 3  4x 2 + 3x  5) = 5x 5  20x 4 + 15x 3  25x 2

8. 1-8 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply each of the following. a) x + 3 and x + 5b) 3x  2 and x  1 Solution a) (x + 3)(x + 5) = (x + 3)x + (x + 3)5 = x(x + 3) + 5(x + 3) = x  x + x  3 + 5  x + 5  3 = x 2 + 3x + 5x + 15 = x 2 + 8x + 15

9. 1-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Solution b) (3x  2)(x  1) = (3x  2)x  (3x  2)1 = x(3x  2)  1(3x  2) = x  3x  x  2  1  3x  1(  2) = 3x 2  2x  3x + 2 = 3x 2  5x + 2

10. Copyright © 2014, 2010, and 2006 Pearson Education, Inc. The Product of Two Polynomials To multiply two polynomials P and Q, select one of the polynomials, say P. Then multiply each term of P by every term of Q and combine like terms.

11. 1-11 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply: (5x 3 + x 2 + 4x)(x 2 + 3x) Solution 5x 3 + x 2 + 4x x 2 + 3x 15x 4 + 3x 3 + 12x 2 5x 5 + x 4 + 4x 3 5x 5 + 16x 4 + 7x 3 + 12x 2

12. 1-12 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply: (  3x 2  4)(2x 2  3x + 1) Solution 2x 2  3x + 1  3x 2  4  8x 2 + 12x  4  6x 4 + 9x 3  3x 2  6x 4 + 9x 3  11x 2 + 12x  4