1 / 25

Bell-ringer

Bell-ringer. Geometry Text. 7.3.2 Products and Factors of Polynomials. Objectives: 1).Divide one polynomial by another using long and synthetic division 2).Use the Remainder Theorem to solve problems. Definitons. Divisor -expression that you divide by

celine
Télécharger la présentation

Bell-ringer

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bell-ringer • Geometry Text

  2. 7.3.2 Products and Factors of Polynomials • Objectives: 1).Divide one polynomial by another using long and synthetic division 2).Use the Remainder Theorem to solve problems

  3. Definitons • Divisor-expression that you divide by • Dividend – the expression being divided • Quotient - the answer after division is complete • Remainder - what is left over after dividing. • Refer to the example

  4. Long Division with numbers 8 647

  5. 20 31 Long Division With Numbers Find the quotient: (23828) ÷ (31) 7 6 8 2 31 238 2 8 8 - 217 768 20/31 or 768 + 20/31 21 - 186 26 - 248 20

  6. Practice with variables • 2x2 ÷ x 9y3÷ 3y • 16w2 ÷4w 36x3÷2x

  7. - 16 x – 4 x2 + 2x – 14 – 16 x – 4 Example Find the quotient: (x3 – 2x2 – 22x + 40) ÷ (x – 4) x2 + 2x – 14 x – 4 x3 – 2x2 – 22x + 40 - (x3 – 4x2) 2x2 – 22x - (2x2 – 8x) –14x + 40 - (–14x + 56) – 16

  8. Example Find the quotient: (x3 –x2 – 4) ÷ (x2 + x + 2) x - 2 x2 + x + 2 x3 –x2 + 0x - 4 - (x3 + x2 +2x) -2x2 – 2x - 4 - (-2x2 – 2x – 4) 0 Quotient: x – 2

  9. Now You • Find the quotient: (x3 + 3x2 – 13x - 15) ÷ (x2 – 2x – 3) Quotient: x + 5

  10. Synthetic Divsion Use synthetic division to find the quotient: (x3 + x2 – 9x - 9) ÷ (x -3) Step 1: Write the coefficients of the polynomial, and the r-value of the divisor on the left 1 -9 -9 1 3

  11. Example 2 Use synthetic division to find the quotient: (x3 + x2 – 9x - 9) ÷ (x -3) Step 2: Draw a line and write the first coefficient under the line. 1 -9 -9 1 1 3 1

  12. Example 2 Use synthetic division to find the quotient: (x3 + x2 – 9x - 9) ÷ (x - 3) Step 3: Multiply the r-value, 3, by the number below the line and write the product below the next coefficient. 1 -9 -9 1 3 3 1

  13. Example 2 Use synthetic division to find the quotient: (x3 + x2 – 9x - 9) ÷ (x - 3) Step 4: Write the sum of 1 and 3 below the line. 1 -9 -9 1 3 3 1 4

  14. Example 2 Use synthetic division to find the quotient: (x3 + x2 – 9x - 9) ÷ (x - 3) Repeat steps 3 and 4. 1 -9 -9 1 3 3 12 1 4 3

  15. Example 2 Use synthetic division to find the quotient: (x3 + x2 – 9x - 9) ÷ (x - 3) Repeat steps 3 and 4. 1 -9 -9 1 3 3 12 9 1 4 3 0

  16. Example 2 Use synthetic division to find the quotient: (x3 + x2 – 9x - 9) ÷ (x - 3) The remainder is 0 and the resulting numbers are the coefficients of the quotient. 1 -9 -9 1 3 3 12 9 1 4 3 0 x2 + 4x + 3

  17. Synthetic Division v. long division *Synthetic Division can only be used when dividing by a linear binomial of the form x –r. **Otherwise long division must be used.

  18. Example Use synthetic division to find the quotient: (x4 – 3x + 2x3 – 6) ÷ (x - 2) -6 2 0 -3 1 2 26 2 8 16 1 4 8 13 20 x3 + 4x2 + 8x + 13 + 20/(x-2)

  19. Now You Use synthetic division to find the quotient: (6x2 – 5x - 6) ÷ (x + 3) -5 -6 6 -3 -18 69 6 -23 63 6x -23 + 63/(x+3).

  20. 2 Example 3 Given that 2 is a zero of P(x) = x3 – 3x2 + 4, use division to factor x3 – 3x2 + 4. Since 2 is a zero, x = 2 , so x – 2 = 0 , which means x – 2 is a factor of x3 – 3x2 + 4. (x3 – 3x2 + 4) ÷ (x – 2) Method 2 Method 1 x2 - x – 2 1 -3 0 4 x – 2 x3 – 3x2 + 0x + 4 2 -2 -4 - (x3 – 2x2) 1 -1 -2 0 -x2 + 0x - (-x2 + 2x) x3 – 3x2 + 4 = (x – 2)(x2 – x – 2) –2x + 4 - (–2x + 4) 0

  21. Practice Given that -3 is a zero of P(x) = x3 – 13x - 12, use division to factor x3 – 13x – 12. x3 -13x -12 = (x + 3)(x2 -3x -4)

  22. Remainder Theorem If the polynomial expression that defines the function of P is divided by x – a, then the remainder is the number P(a).

  23. 6 Example 4 Given P(x) = 3x3 – 4x2 + 9x + 5 find P(6) by using both synthetic division and substitution. Method 2 Method 1 3 -4 9 5 P(6) = 3(6)3 – 4(6)2 + 9(6) + 5 = 3(216) – 4(36) + 54 + 5 18 84 558 3 14 93 563 = 648 – 144 + 54 + 5 = 563

  24. Practice Given P(x) = 3x3 + 2x2 + 3x + 1 find P(-2) using synthetic division and substitution.

  25. Homework p.446 #72 – 96 by 3’s

More Related