1. 3.6 Day 2 Why Synthetic Division? What use is this method, besides the obvious saving of time and paper?

2. To see what is really going on, lets look at some different problems. 1. If then find F(1) 2. Find What do you notice? Lets try again.

3. 1. If then find F(2) 2. Find What do you notice? Now lets look at the two theorems that follow from this.

4. The Remainder Theorem If is not a factor of F(x), then F(c) = remainder when F(x) is divided by That is

5. The Factor Theorem If is a factor of F(x) then F(c) = 0. What does that mean? Note: Roots = Zeroes

6. How does this apply? 1.Find F(12) if 2.Is (x – 2) a factor of

7. What else can we do with this? Try this: 1. Factor 765 2. Factor 3. Solve 4. Find the polynomial that has as roots 1, -1 and 7