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Bell Work Week #16

Bell Work Week #16. (12/4/13) Divide using long division. You’ve got 3 minutes. 1. 161 ÷ 7 2. 277 ÷ 12. 3.3 Dividing Polynomials. Objective : Students will be able to use long division and synthetic division to divide polynomials and will be able to complete synthetic substitution. .

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Bell Work Week #16

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  1. Bell Work Week #16 • (12/4/13) Divide using long division. You’ve got 3 minutes. • 1. 161 ÷ 7 • 2. 277 ÷ 12

  2. 3.3 Dividing Polynomials Objective: Students will be able to use long division and synthetic division to divide polynomials and will be able to complete synthetic substitution.

  3. Dividing polynomials by long division • Step 1: Write the problem in standard form, and replace any missing degrees with a place holder. • (For ex, 4x3 + 2x2 + 5 becomes 4x3 + 2x2 + 0x + 5) • Step 2: Write the problem in long division form. • Step 3: Divide. • Example 1: (15x2 + 8x – 12) ÷ (3x + 1)

  4. Example 2: (4x2 + 3x3 + 10) ÷ (x – 2)

  5. Your turn… • Example 3: (x2 + 5x – 28) ÷ (x – 3)

  6. Homework for tonight • Homework # ____ • Textbook pg. 170 #13, 14, 16

  7. Vocabulary • Synthetic division – a shorthand method of dividing a polynomial by a linear binomial by using only the coefficients (numbers in front of the variables). • For synthetic division to work • A. the polynomial must be written in standard form with 0 used as a place holder for any missing degrees • B. the divisor must be written in the form (x – a) • * (dividend) ÷ (divisor)

  8. Divide the following polynomials using synthetic division • Example 1: (x2 – 3x – 18) ÷ (x – 6)

  9. Example 2 • (6x2 – 5x – 6) ÷ (x + 3)

  10. Example 3 • (x4 – 2x3 + 3x + 1) ÷ (x – 3)

  11. Example 4 • (4x2 – 12x + 9) ÷ (x + ½)

  12. Homework for tonight • Homework # ____ • Textbook pg. 170 #19 – 24

  13. 3.3 Part 3 – Synthetic Substitution Objective: I can use synthetic substitution to evaluate polynomials.

  14. About Synthetic Substitution… • You can use synthetic division to evaluate polynomials at certain values. This process is called synthetic substitution. • The process of synthetic substitution is EXACTLY the same process as synthetic division, you just look at the final answer differently. • Remainder Theorem – If the polynomial function P(x) is divided by x – a, then the remainder r is P(a).

  15. Use synthetic substitution to evaluate the polynomial for the given value. • Example 1: P(x) = x3 + 3x2 + 4 for x = -3

  16. Example 2: P(x) = x3 – 4x2 + 3x – 5 for x = 4

  17. Example 3: P(x) = 5x2 + 9x + 3 for x = 1/5

  18. Homework for tonight • HW #22 – Textbook pg. 170 #25 – 28

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