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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.5 Dividing Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1.

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Presentation on theme: "Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.5 Dividing Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1."— Presentation transcript:

1 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.5 Dividing Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

2 2

3 3 When dividing exponential expressions with the same nonzero base, subtract the exponent in the denominator from the exponent in the numerator. Use this difference as the exponent on the common base. The Quotient Rule

4 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 4 Objective #1: Example

5 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 5 Objective #1: Example

6 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 6 Objective #1: Example

7 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 7 Objective #1: Example

8 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 8

9 9 If b is any real number other than 0, The Zero Exponent Rule

10 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 10 Only 2 is raised to the 0 power. 2xy is raised to the 0 power. Only y is raised to the 0 power. 5 is raised to the 0 power. Zero as an ExponentEXAMPLES Simplify:

11 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Only 2 is raised to the 0 power. 2xy is raised to the 0 power. Only y is raised to the 0 power. 5 is raised to the 0 power. Zero as an ExponentEXAMPLES Simplify:

12 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 12 Objective #2: Example

13 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 13 Objective #2: Example

14 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 14 Objective #2: Example

15 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 15 Objective #2: Example

16 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 16 Objective #2: Example

17 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 17 Objective #2: Example

18 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 18

19 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 19 If a and b are real numbers and b is nonzero, then When a quotient is raised to a power, raise the numerator to the power and divide by the denominator raised to the power. Quotients to Powers Rule for Exponents

20 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 20 Cube the numerator and denominator. Square the numerator and denominator. Quotients-to-Powers Rule for ExponentsEXAMPLES Simplify:

21 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 21 Cube the numerator and denominator. Square the numerator and denominator. Quotients-to-Powers Rule for ExponentsEXAMPLES Simplify:

22 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 22 Cube the numerator and denominator. Cube each factor in the numerator. Simplify. Quotients to Powers RuleEXAMPLE Simplify:

23 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 23 Cube the numerator and denominator. Cube each factor in the numerator. Simplify. Quotients to Powers RuleEXAMPLE Simplify:

24 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 24 Objective #3: Example

25 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 25 Objective #3: Example

26 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 26 Objective #3: Example

27 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 27 Objective #3: Example

28 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 28

29 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 29 To divide monomials, divide the coefficients and then divide the variables. Use the quotient rule for exponents to divide the variable factors: Keep the variable and subtract the exponents. Dividing Monomials

30 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 30 Divide the coefficients, 5/10 = 1/2, then divide the variables by subtracting exponents. Simplify. Dividing MonomialsEXAMPLE

31 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 31 Divide the coefficients, 5/10 = 1/2, then divide the variables by subtracting exponents. Simplify. Dividing MonomialsEXAMPLE

32 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 32 Divide the coefficients, 6/2 = 3, then divide the variables by subtracting exponents. Simplify. Dividing MonomialsEXAMPLE

33 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 33 Divide the coefficients, 6/2 = 3, then divide the variables by subtracting exponents. Simplify. Dividing MonomialsEXAMPLE

34 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 34 Objective #4: Example

35 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 35 Objective #4: Example

36 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 36 Objective #4: Example

37 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 37 Objective #4: Example

38 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 38

39 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 39 Objective #5: Example From 4b.

40 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 40 Objective #5: Example From 4b.

41 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 41

42 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 42 Division of Polynomials Dividing a Polynomial That Is Not a Monomial by a Monomial To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

43 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 43 Division of PolynomialsEXAMPLE Divide: SOLUTION Express the division in a vertical format. Divide each term of the polynomial by the monomial. Note the 3 separate quotients. Simplify each quotient.

44 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 44 Divide the coefficients, then divide the variables by subtracting exponents. Divide each term of the polynomial by the monomial. Simplify. Dividing a Polynomial by a Monomial

45 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 45 Divide the coefficients, then divide the variables by subtracting exponents. Divide each term of the polynomial by the monomial. Simplify. Dividing a Polynomial by a Monomial

46 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 46 Objective #6: Example

47 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 47 Objective #6: Example

48 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 48 Objective #6: Example

49 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 49 Objective #6: Example


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