5. Polynomials

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5.01a Introducing Cubics and y=x^3

5.01b Introducing the General Equation for a Cubic

5.02a An Example of Expanding Triple Brackets

5.02b Another Example of Expanding Triple Brackets

5.03 Sketching a Translation of y=x^3

5.04a Sketching a Cubic that is the Product of Three Linear Terms

5.04b An Easy Example of Sketching a Cubic

5.04c Another Example of Sketching a Cubic

5.04d An Example of Sketching a Cubic when a is negative

5.04e Sketching a Cubic with a Repeated Root

5.04f Sketching a Cubic with a Repeated Root when a is negative

5.04g EXTENSION: Sketching y = (x + 4)(x^2 +2x + 9)

5.05 Introducing Function Notation

5.06a Introducing the Factor Theorem

5.06b Introducing the Remainder Theorem

5.06c An example of using the Factor Theorem

5.06d An example of using the Remainder Theorem

5.07a Introducing Polynomial Division

5.07b Polynomial Division with a zero remainder

5.07c Polynomial Division with a non-zero remainder

5.07d A Trickier Example of Polynomial Division

5.07e An Alternative Layout for Polynomial Division

5.08 Expressing a Cubic as a Product of Three Linear Factors

5.09 Cubic Equation - Factor Theorem - Polynomial Division - Sketch

5.10 A Problem that utilises both the Factor Theorem and the Remainder Theorem