S5 Pol 4 Remainder and Factor Theorem

Stage 5 Mathematics Remainder and Factor Theorem

Success Criteria

State the remainder and factor theorems.

Apply the factor theorem and other techniques to factorise and solve polynomial equations.

State the maximum number of zeroes a polynomial may have and use reasoning to explain how many zeroes the  polynomial has.

 

Introductory Notes

Remainder and Factor Theorem Notes.pdf Download Remainder and Factor Theorem Notes.pdf 

Introductory Video

Definitions

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Open Ended Task

Open Ended Task

A polynomial of degree 3 has two integer roots and one rational root. The polynomial also has a constant term with a value of 36. Write down three polynomials in expanded form that match this description, explain your reasoning for each polynomial.

Enabling Prompt

1. Factorise LaTeX: y=2x^2+7x-4y=2x2+7x−4 and state the values for LaTeX: xx when LaTeX: y=0y=0

Extending Task

A polynomial of degree 4 has two integer roots only. The polynomial also has a constant term with a value of 36. Write down three polynomials in expanded form that match this description, explain your reasoning for each polynomial.

Solution

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Consolidating Task

A polynomial of degree 3 has one integer roots and two rational root. The polynomial also has a constant term with a value of 24. Write down three polynomials in expanded form that match this description, explain your reasoning for each polynomial.

Consolidating Task Solution

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Check Your Understanding