Polynomial ArithmeticMr. McOwen

Warm-Up

• For the following polynomial functions:a. What is the maximum number of local extrema for the following functions?b. What is the minimum number of local extrema for the following functions?

•A.•B.

Addition/Subtraction:Polynomial Arithmetic

can use horizontal or vertical methods for each

To add or subtract polynomials, add or subtract the coefficients of terms with the same degree. You can use a horizontal or vertical format.

Ex. 1

a.

b.

What is:

What is:

Ex. 2

a.

b.

Warm-Up• For the following polynomial functions:

What is the maximum / minimum number of local extrema for the following functions?

•A.•B.

• If and What is

Warm-Up• For the following polynomial functions:

What is the maximum / minimum number of local extrema for the following functions?

A.•What is the maximum/minimum number of

zeros for:B. and C.

can use horizontal or vertical methods for each

Multiplication:

Ex. 1

To multiply two polynomials together we use the distributive property.

What is:

Ex. 2

The graph of a polynomial function is continuous.The graph of a polynomial function has only smooth turns. A function of n degrees has at most n – 1 turns.

Characteristics of Graphs of Polynomial Functions

Graphs of Polynomials

Graph the following:

x³ vs x5��

x² vs x4

Worksheet – end behaviorPages 467-6815-20 all25-30 all43-48 all

Classwork and Homework

1.) 2.)

3.)

Use Synthetic Substitution to evaluate each of the following:

, find4.)

, find5.)

Evaluating with i and square root

, find

Evaluate each of the following:

, find

, find

, find