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

5.7 Dividing Polynomials Divide a polynomial by a monomial. Divide a polynomial by a polynomial. 1 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Divide a polynomial by a monomial. Objective 1 Divide a polynomial by a monomial. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 3

Dividing a polynomial by a monomial. We add two fractions with a common denominator as follows. In reverse this statement gives a rule for dividing a polynomial by a monomial: To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: Examples: and Divisor Dividend Quotient Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 4

EXAMPLE 1 Divide 12m6 + 18m5 + 30m4 by 6m2. Solution: Dividing a Polynomial by a Monomial Divide 12m6 + 18m5 + 30m4 by 6m2. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 5

EXAMPLE 2 Divide Solution: Dividing a Polynomial by a Monomial Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 6

EXAMPLE 3 Divide −8p4 − 6p3 − 12p5 by −3p3. Solution: Dividing a Polynomial by a Monomial with a Negative Coefficient EXAMPLE 3 Divide −8p4 − 6p3 − 12p5 by −3p3. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 7

EXAMPLE 4 Divide Solution: Dividing a Polynomial by a Monomial Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 8

Divide a polynomial by a polynomial. Objective 2 Divide a polynomial by a polynomial. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 9

Divide a polynomial by a polynomial. To divide a polynomial by a polynomial (other than a monomial). Both polynomials must first be written in descending powers. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 10

Divide a polynomial by a polynomial. (cont’d) Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 11

EXAMPLE 5 Divide Solution: Dividing a Polynomial by a Polynomial Remember to include “ ” as part of the answer. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 12

EXAMPLE 6 Divide x3 − 8 by x − 2. Solution: Dividing into a Polynomial with Missing Terms Divide x3 − 8 by x − 2. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 13

EXAMPLE 7 Divide Solution: Dividing by a Polynomial with Missing Terms Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 14

EXAMPLE 8 Divide 3x3 + 7x2 + 7x + 11 by 3x + 6. Solution: Dividing a Polynomial when the Quotient Has Fractional Coefficients EXAMPLE 8 Divide 3x3 + 7x2 + 7x + 11 by 3x + 6. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5.7 - 15