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
Download this file (12.3.1.notes.pdf)12.3.1.notes.pdfNotes: Properties of Polynomial Functions852 kB

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
Attachments:
FileDescriptionFile size
Download this file (12.3.2.notes.pdf)12.3.2.notes.pdfNotes: Long Division of Polynomials502 kB

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

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
Attachments:
FileDescriptionFile size
Download this file (12.3.3b.notes.factoring.pdf)12.3.3b.notes.factoring.pdfNotes: Factoring Polynomials607 kB

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
Download this file (12.3.4.notes.pdf)12.3.4.notes.pdfNotes: Equations and Graphs2194 kB

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
Attachments:
FileDescriptionFile size
Download this file (12.3.4b.notes.pdf)12.3.4b.notes.pdfNotes: Equations and Graphs part B908 kB
   
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