1. 6-5: The Remainder and Factor Theorems Objective: Divide polynomials and relate the results to the remainder theorem.

3. Example 1

5. Remainder Theorem

6. Synthetic Division: A process for division of a polynomial by a binomial. Example 2: Divide

7. Step 1: Write the terms of the polynomial in descending order. Then write just the coefficients as shown.

8. Step 2: Write the constant k, of the divisor x – k to the left Bring the first coefficient down. Multiply the first coefficient by k and write the product under the second coefficient. Add the second column. Write the sum as shown.

9. To write the result

10. Example 3:

11. Factor Theorem

12. Example 4 x = 2 Subtract 2 from both sides x – 2 = 0 So, x – 2 is a factor

14. The result gives the coefficients of the quotient.

16. HOMEWORK: AM Objectives #81 Divide Polynomials #82 Long division, factor higher term polynomials

17. Example 4 Factor

18. Use synthetic division to find the other factors. The result gives the coefficients quotient