Description of the form of a polynomial function

• Identifying polynomial functions

• Characteristics of polynomial functions

• Graphs of polynomial functions

  • Shape and its relationship to degree

• Sketching polynomial functions (3 steps)

  • Understanding end behaviours for various functions

  • Understanding turning points for various functions

  • Understanding zeros for various functions

• Sample questions solved to solidify understanding

• Sample question to practice graphing polynomial functions

• More solutions to sample questions

Lesson 2: Polynomial Functions in Factored Form

• 3 key points to determine before sketching

• Sketching polynomial functions

• Sketching a cubic function with 2 zeros, order 2

• Determining a polynomial function given the graph

  • Determining domain and range

  • Sketching a graph of a different kind of polynomial function

Lesson 3: Cubic & Quartic Functions

• Example to find transformed points, given:

  • Parent function passing through 3 points

  • 2 separate transformations

• Transformation of a graph to determine roots of another

Lesson 4: Dividing & Factoring Polynomials

• Review of long division steps

• Division of a cubic polynomial by a binomial

• Synthetic Division explained:

  • Creation of a chart

  • Isolation of coefficients

  • Identifying the “k” factor

  • Dealing with missing ‘order terms’

• Determining factors of polynomials:

  • Identify “k”

  • Use Synthetic Division

• Determining whether a polynomial is divisible by a binomial expression

  • Identify “k”

  • Test for remainder of zero or

  • Substitute the value into the equation

Lesson 5: Factoring Sum & Differences of Cubes

• Recall Difference of Squares

• Recall sun and difference of cubic equations

• Examples of simple factoring questions

• Examples of more difficult factoring questions

Lesson 6: Solving Polynomial Inequalities

• 5 steps to solving Polynomial Inequalities

• Example solving a cubic inequality

  • All 5 steps carefully explained

• Example solving a quartic inequality

• Example solving a quartic inequality with missing terms

Here are a few sample questions for you to practice. The answers are given at the end.