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

2. 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, 4x 3 + 2x 2 + 5 becomes 4x 3 + 2x 2 + 0x + 5) Step 2: Write the problem in long division form. Step 3: Divide. Example 1: (15x 2 + 8x – 12) ÷ (3x + 1)

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

5. Your turn… Example 3: (x 2 + 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: (x 2 – 3x – 18) ÷ (x – 6)

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

10. Example 3 (x 4 – 2x 3 + 3x + 1) ÷ (x – 3)

11. Example 4 (4x 2 – 12x + 9) ÷ (x + ½)

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

13. 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) = x 3 + 3x 2 + 4 for x = -3

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

17. Example 3: P(x) = 5x 2 + 9x + 3 for x = 1/5

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