1. Sect. 2-2 Synthetic Division; The remainder and Factor theorems Objective: SWBAT use the synthetic division and to apply the remainder and factor theorems.

2. Using Long Division In earlier Algebra we use Long Division to find the remainder

3. Example 5:

4. Exercise #18

5. C.) Synthetic Division 2 4 0 1 7 4 2 4 8 8 2 4 0 1 7 816 4 8 17 2 4 0 1 7 816 4 8 17 34 41 Quotient Remainder Writing the 2 of x -2 and the coefficients of the dividend Bringing down the first coefficient Multiplying 4 by 2 to get 8 and Adding 0 and 8 Multiplying 8 by 2 to get 16 and Adding 1 and 16 Multiplying 17 by 2 to get 34 and Adding 7 and 34

6. Example 2: Use synthetic Division to find the quotient and remainder Writing the 2 of x -2 and the coefficients of the dividend 21 6 - 1 -30 2 1 8 16 15 30 0 Using Synthetic Division

7. Example 3: Use synthetic Division -2 8 0 -6 0 1 - 8 8 -16 32 26 -52 104 105 -210 -218

8. The Remainder Theorem When a polynomial P(x) is divided by x – a the remainder is P(a) The Factor Theorem For a polynomial P(x) x – a is a factor If and only If P(a) = 0

9. Example of the remainder theorem by 1 1 -2 5 1 1 1 -1 -1 4 4 5

10. Example of the Factor Theorem Any time you can divide and get a 0 for a remainder then you have an illustration of the factor theorem. -1 1 -2 0 5 2 1 -3 3 3 2 -2 0

11. Finding the remaining roots 3 2 -5 -4 3 2 6 1 3 -3 0

12. Homework 1,3,4,5,11,15,19,20 pg. 61