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

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Presentation transcript:

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

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.

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

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

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

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

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