Solving Higher Degree Polynomial Equations.

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Presentation transcript:

Solving Higher Degree Polynomial Equations

Let

Has Degree zero Has Degree one Has Degree two Has Degree three ? Has Degree

A Polynomial Function of Degree n in one variable x , where

Has NO zeros Has ONE zero Has TWO zeros Has THREE zeros Has n zeros

Go Back

A Polynomial Function of Degree n in one variable x , where Has Exactly n zeros

How Many Zeros Should We Expect ? 5

Ex 1 ZEROS How Do I Do That? FACTOR

Ex 1 ZEROS GCF

Ex 1 ZEROS

Ex 1 ZEROS

Ex 1 ZEROS

Ex 1 ZEROS

Ex 1 ZEROS

Ex 1 ZEROS Completely Factored ? NO

Ex 1 ZEROS Linear Factors

Ex 1 ZEROS

Ex 1 FIND THE ZEROS

Ex 1

Ex 1

Ex 1

Ex 1

Ex 1

Ex 1

Ex 1 Zeros

Ex 1 Zeros

Ex 1 Zeros

Ex 1 How Many Zeros ? 5 Zeros

Next Example

How Many Zeros Should We Expect ? 4

Ex 2 ZEROS FACTOR

Ex 2 ZEROS

Ex 2 Dummy Out ZEROS You Finish

Ex 2 ZEROS

Ex 2 ZEROS 4 Zeros How Many Zeros ?

Ex 2 4 Zeroc How Many Zeros ?

Next Example

How Many Zeros Should We Expect ? 3

Ex 3 ZEROS ? Try Grouping

Ex 3 ZEROS

Ex 3 ZEROS

Ex 3 ZEROS

Ex 3 FACTOR NO

Ex 3

Ex 3 You Finish

Ex 3

Ex 3 How Many Zeros ? 3 Zeros

Ex 3 How Many Zeros ? 3 Zeros

Next Example

How Many Zeros Should We Expect ? 6

Try The Difference of Two Squares Ex 4 ZEROS Try The Difference of Two Squares

Ex 4 ZEROS The Sum of Two Cubes

The Difference of Two Cubes Ex 4 ZEROS The Difference of Two Cubes

Ex 4 ZEROS

Ex 4 ZEROS Factorable? NO

Ex 4 ZEROS

Ex 4 ZEROS

Ex 4 ZEROS

Ex 4 ZEROS

Ex 4 ZEROS

Ex 4 Quadratic Formula Quadratic Formula

Ex 4

Ex 4 ZEROS

Ex 4 How Many Zeros ? 6 ZEROS

Ex 4 How Many Zeros ? 6 ZEROS