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4.7 Dividing Polynomials

4.7 Dividing Polynomials. Objective 1 . Divide a polynomial by a monomial. Slide 4.7-3. Dividing a polynomial by a monomial. We add two fractions with a common denominator as follows. . a c. b c. a b c. . . In reverse this statement gives a rule for dividing a polynomial by a

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4.7 Dividing Polynomials

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  1. 4.7 Dividing Polynomials

  2. Objective 1 Divide a polynomial by a monomial. Slide 4.7-3

  3. Dividing a polynomial by a monomial. We add two fractions with a common denominator as follows.  a c b c a b c   In reverse this statement gives a rule for dividing a polynomial by a monomial: Dividing A Polynomial by a Monomial To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: a b a b c c c 2 5 2 5 3 3 3       0 . c Dividend   3 y 3 2 y x z x z     Examples: and Quotient 2 2 y Divisor Slide 4.7-4

  4. CLASSROOM EXAMPLE 1 Dividing a Polynomial by a Monomial Divide 12m6 + 18m5 + 30m4 by 6m2. Solution:   6 5 4 12 18 6 18 6 30 m m m m  2 6 5 4 12 6 30 6 m m m m m m    2 2 2    4 3 2 2 3 5 m m m Slide 4.7-5

  5. CLASSROOM EXAMPLE 2 Dividing a Polynomial by a Monomial   4 3 50 30 10 20 m m m m Divide . 3 Solution: 4 3 50 10 30 10 20 10 m m   m m m 2 m m m    3 3 3  2 5 3 2 m    5 3 m 2 Slide 4.7-6

  6. CLASSROOM EXAMPLE 3 Dividing a Polynomial by a Monomial with a Negative Coefficient Divide −8p4− 6p3 − 12p5 by −3p3. Solution:     5 4 3 12 8 3 6 p p p p  3      5 4 3 12 3  8 3 6 3 p p p p p    3 3 3 p 8 p    2 4 2 p 3 Slide 4.7-7

  7. CLASSROOM EXAMPLE 4 Dividing a Polynomial by a Monomial   4 3 3 2 2 45 30 15 60 x y x y x y x y Divide . 2 Solution:  4 3 3 2 2 45 15 30 15 60 15 x y x y x y x y x y x y    2 2 2    2 2 3 2 4 x y xy Slide 4.7-8

  8. Objective 2 Divide a polynomial by a polynomial. Slide 4.7-9

  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. Slide 4.7-10

  10. Divide a polynomial by a polynomial. Slide 4.7-11

  11. CLASSROOM EXAMPLE 5 Dividing a Polynomial by a Polynomial   2 2 5  25. x x Divide 5 x Solution:  2x 5      x   2 5 2 5 10 5 5  25 x x x x 2 2 25 25 x x x 2 5 0 Slide 4.7-12

  12. CLASSROOM EXAMPLE 6 Dividing a Polynomial by a Polynomial     3 2 2 5 2 13. x x x x Divide 3  1 Solution:   2x 4 x  2 3 x       2  3 2 2 3 2 5 13 x x x x 3 2 2 x 3 2 x x x   2 5 3 8 8 x x x x 2 13 12 1 1    2 4 x x  2 3 x Remember to include “ ” as part of the answer. remainde div r  isor Slide 4.7-13

  13. CLASSROOM EXAMPLE 7 Dividing into a Polynomial with Missing Terms Divide x3− 8 by x − 2. Solution:   2x 2x 4      3 2 2 0 2 2 2 0 8 x x x x x x x x 3 2   2 0 4 4 4 x x x x 2 8 8 0   2 2 4 x x Slide 4.7-14

  14. CLASSROOM EXAMPLE 8 Dividing by a Polynomial with Missing Terms     5 4 3 2 2 6 3 18. m m m  m Divide 2 3 m Solution:   6 2 3 2m m        3   2 5 4 3 2 0 3 2 2 6 6 3 0 18 m m m m m 0 m m m m 5 4 m     4 3 2 0 0 3 3 m m m m m m 4 3 2       2 6 6 0 0 18 18 m m m m 2   3 2 0 2 6 m m Slide 4.7-15

  15. CLASSROOM EXAMPLE 9 Dividing a Polynomial When the Quotient Has Fractional Coefficients Divide 3x3+ 7x2+ 7x + 11 by 3x + 6. Solution: 1 3x 5 3 1  2x    3 6 x      3 2 3 6 3 7 6 7 11 x x x x x x 3 2 3   2 7 2 x x x x 2 x x 5 5 11 10 1 3 5 3 1     2 x x 3 6 x 1 Slide 4.7-16

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