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Dividing Polynomials

Dividing Polynomials. WOW! I want to learn how to do that?. Why would you want to do that?. What do you find when you divide 15 by 5?. What do you find when you divide ( 6x 3 – 5x 2 – 12x – 4 ) by (3x+2)?. You find 3, the other factor of 15. You find 2x 2 – 3x – 2, another

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Dividing Polynomials

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  1. Dividing Polynomials WOW! I want to learn how to do that? Why would you want to do that? What do you find when you divide 15 by 5? What do you find when you divide ( 6x3 – 5x2 – 12x – 4 ) by (3x+2)? You find 3, the other factor of 15 You find 2x2 – 3x – 2, another factor of the polynomial. Which you can then factor into (2x+1)(x-2)

  2. D M S B 2x2 – 3x – 2 3x + 2 6x3 - 5x2 – 12x – 4 6x3 + 4x2 -9x2 – 12x -9x2 – 6x – 6x – 4 – 6x – 4 0 Check: (3x + 2)(2x2 – 3x – 2) = 6x3 – 9x2 – 6x + 4x2 – 6x – 4 6x3 – 5x2 – 12x – 4

  3. – 7 (2x – 1) 2x2 – 3x + 1 2x – 1 4x3 – 8x2 + 5x – 8 4x3 – 2x2 + 5x -6x2 -6x2 + 3x 2x - 8 2x – 1 remainder - 7 Check: (2x – 1)(2x2 – 3x + 1) = 4x3 – 6x2 + 2x – 2x2 + 3x – 1 = 4x3 – 8x2 + 5x – 1 Add remainder -7 = 4x3 – 8x2 + 5x – 8

  4. x2 + 3x 5x4 + 18x3 + 8x2 – 3x + 9x2 3x3 + 3x – 1 5x2 5x4 + 15x3 3x3 + 8x2 – x2 – 3x – x2 – 3x 0

  5. Synthetic Division: Your divisor must be x - # Who’s in the house? ┘ Write the coefficients using zeros if needed. Drop it like it’s hot! (one time) Multiply by the house, then add. (repeat)

  6. Synthetic Division 3 2 1 (3x3 + 8x2 + 5x – 7)  (x + 2) 3 8 5 -7 -2 -6 -4 -2 3 2 1 -9 remainder 9 x + 2 – + x2 + x answer

  7. Synthetic Division (3x4 + 13x3 + 2x2 - 3x + 20)  (x + 4) 13 20 3 2 -3 -4 -12 -4 -20 8 5 1 3 -2 0 remainder 3 1 - 2 5 answer + x2 x3 + x

  8. -120 0 6 0 -18 2 0 120 48 12 60 24 0 6 24 30 12 60

  9. Synthetic Division (x4 – 5x2 – 36)  (x – 3) 3 1 0 -5 -36 0 3 36 9 12 remainder 0 1 3 4 12 answer  (x + 3) x3 + 3x2 + 4x + 12 -3 1 3 4 12 0 -12 -3 Imaginary factors 0 x2 + 4 1 0 4

  10. Synthetic Division 2 3 -13 3 - 7 3 2 3 10 3 -2 3 - 2 3 (3x3 – 13x2 – 7x + 2)  (3x + 2) 1 1 -5 1 0 remainder answer x2 – 5x + 1

  11. Synthetic Division 1 2 (4x3 – 8x2 + 3x – 8)  (2x – 1) 3 2 2 -4 -4 -3 2 1 0 -4 2 -3 0 remainder 4 (2x – 1) answer 2x2 – 3x –

  12. x2 + 3x One factor is + 3x – 1 5x2 x = = .24 and x = = -.84 Factor: 5x4 + 18x3 + 8x2 - 3x Divide to find that the other factor is: Connection: thesolutionsto 5x4 + 18x3 + 8x2 - 3x = 0 are … x = 0 and x = -3 and =

  13. Synthetic Division 1 3 -1 3 -7 3 -2 3 1 3 ( 6x2 – x – 7)  (3x + 1) 2 2 -1 -2 remainder answer 2 (3x + 1) 2x – 1 –

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