## 12.3.1 Properties of Polynomial Functions

Polynomial functions can be categorized as even or odd, based on the degree of the polynomial.  They have a number of common characteristics based upon their classification.

Resources:

• Notes:Properties of Polynomial functions

Assignment:

• p. 114 #1-9, C1, C2  *11, 12

Things you should be able to do after today

• identify a polynomial function from its equation and / or graph
• explain the role of the leading coefficient and the constant term with respect to the graph
• be able to generalize rules of graphing odd or even degree functions
• solve a problem by modeling a situation using a polyomial function and analyzing the graph
Attachments:
FileDescriptionFile size 12.3.1.notes.pdfNotes: Properties of Polynomial Functions852 kB

## 12.3.2b Remainder Theorem/Factor Theorem

If you are only interested in finding out the remainder when a polynomial is divided by a binomial, then we can use the remainder theorem.  This is a great way to find binomial factors of a polynomial!

Resources

Assignment:

• p124 #6-10, C2, C3 *14, 15, 16
• p133 #1-4, 7, C1

Things you should know after today:

• What is the remainder theorem
• How can the remainder theorem be used to find factors of a polynomial

## 12.3.3b Factoring Polynomials

Using the factor throrem and synthetic division is a way to factor higher degree polynomials.  Once a factor is identified, synthetic division is used to break down the polyomial into 2 factors, at which point one of the factors can be further explored using factor theorem and synthetic division.

See some examples of this process in today's notes:

Resources

• 12.3.3b Notes: Factoring Polynomials

Assignment

• p133 #5, 8, 11, 13, C2 C3

After today you should be able to:

• Identify at least one factor of a polynomial using the integral zero theorem and the factor theorem
• determine the other factor by long division or synthetic division
• repeat the process until you have no more identifiable factors

## 12.3.4a Equations and Graphs of Polynomial Functions

The graph of a polynomial function is easy to relate to its factored form.

Resources

• Notes

Assignment

• p147 #1-4, 7-10, 14 C1 C2 C3

Things you should be able to do after today:

• relate the factored form to the graph of a polynomial
• sketch the graph of a polynomial based on its factored form
• explain how the multiplicity of a factor affects the shape of the graph near it's zeroes
Attachments:
FileDescriptionFile size 12.3.4.notes.pdfNotes: Equations and Graphs2194 kB