Polynomial Functions

Advanced Functions
MHF4U1 (Grade 12 University Preparation)

Introduction to Polynomial Functions

Concepts

  • definition of a polynomial expression
  • degree of a polynomial expression
  • leading coefficient of a polynomial expression
  • names and shapes of polynomial functions
  • properties for describing polynomial functions
  • finite differences of polynomial functions

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Characteristics of Polynomial Functions

Concepts

  • end behaviour of polynomial functions
  • zeros of polynomial functions
  • turning points of polynomial functions

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Polynomial Functions in Factored Form

Concepts

  • equations of polynomial functions in factored form
  • zeros of polynomial functions
  • sketching graphs of polynomial functions
  • determining equations of polynomial functions
  • order of factors of polynomial functions
  • families of polynomial functions

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Dividing Polynomials

Concepts

  • dividing polynomials using long division
  • dividing polynomials using synthetic division

Factoring Polynomials

Concepts

  • the Remainder Theorem
  • the Factor Theorem
  • factoring polynomials
  • determining zeros of polynomial functions
  • sketching graphs of polynomial functions

Student Resources

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Factoring Sums and Differences of Cubes

Concepts

  • factoring sums of cubes
  • factoring differences of cubes
  • functions involving sums and differences of cubes

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TRANSFORMATIONS OF y=x³ AND y=x

Concepts

  • applying combinations of transformations to the graphs of y=x³ and y=x

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Unit Review

Concepts

  • review of all concepts covered in the Polynomial Functions unit

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