Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
- No direct alignment recorded
New NZC (2026)
NZC26-P4-ALG-ER-P-Y10-03
Resources
- CorbettMaths - Factor TheoremQuestions PDF · Answers
Terminology
- Polynomial
- Degree
- Coefficient
- Remainder theorem
- Factor theorem
- Linear factor
- Synthetic division
- Polynomial long division
- Root
Task goals
- Foundation: Evaluate a polynomial P(x) at a given value and use the remainder theorem to state the remainder when P(x) is divided by a linear factor (x-a), without performing full division.
- Proficient: Apply the factor theorem to test whether a given linear expression is a factor of a cubic polynomial, then use polynomial long division (or synthetic division) to fully factorise the polynomial into linear factors.
- Excellence: Solve cubic (or higher-degree) polynomial equations by combining the factor theorem with algebraic techniques, including problems with an unknown coefficient that must be found using a given factor or remainder condition.
Where this fits
What leads into this objective, and where it goes next.
Before
Solving Quadratic Equations by Factorising (Null Factor Law)
Solving Factorised Equations (Null Factor Law)
Solving quadratics
You are here
The Remainder and Factor Theorems
Next
Year 10 is the last year of this phase — the curriculum lists nothing after this. No extension resources on the site yet.
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.