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

Polynomials can be divided using long division (remember long division from grade 4?) and synthetic division.

Resources:

- Notes

Assignment

- p124 #3-5,11,12,13, C1

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

- Watch the notes on Youtube.
- Notes: Includes notes on the remainder theorem and the factor theorem.

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

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

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

Transformations can be applied to polynomial functions as well; we just need to plot more key points to get a better idea of the shape of the transformed graph.

Resources

- Notes

Assignment

- p147 #5, 6, 11, 12, 13, 15, 17 *21,23