1. The Remainder and Factor Theorems

2. Solve by Using Long Division Example 1Example 2

3. How Might You Solve The Following Examples? Example 1Example 2

4. Factoring Polynomial Functions Using Long Division Based on the previous examples, how might you solve the following equation?

5. Solve by Using Long Division Example 1Example 2

6. Factoring Polynomial Functions Using Long Division Based on the previous examples, how might you solve the following equation?

7. Remainder Theorem If a polynomial P(x) is divided by x-r, the remainder is a constant P(r), and P(x)=(x-r) Q(x) + P(r), where Q(x) is a polynomial with degree one less than the degree of P(x). From our previous example this means, P(x)=(x-2) (2x²+3x-8) + 6

8. Synthetic Division Synthetic division is a shortcut for dividing a polynomial by a binomial of the form x - r

9. Divide by Using Synthetic Division

10. Factor Theorem The binomial x - r is a factor of the polynomial P(x) if and only if P(r)=0

11. Practice Problems Divide using synthetic division.

12. Practice Problems Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial.