1. Section 4-3 The Remainder and Factor Theorems

2. Remainder Theorem Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant, P(r), and where Q(x) is a polynomial with degree one less than the degree of P(x).

3. Example 1

4. Synthetic Division by x+3 Remainder 13

6. Divide using synthetic division. By y+2

7. Divide using synthetic division. By y+2 - 2 -1 0 4 0 3 2 0 2 -4 0 0 -6 8 -1 2 0 0 3 -4 8 Remainder of 8

8. Divide using synthetic division. By (x+2)

9. Divide using synthetic division. By (x-1)

10. Divide using synthetic division. By (x+1)

11. Divide using synthetic division. By (x-4)

12. Example 3

13. Example 4

14. Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial by (x+1)

15. Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial by (x+4)

16. Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial by (x-1)

17. Use the remainder and factor theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial by (x-4)

19. Example 5