Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
NA5-7
New NZC (2026)
NZC26-P4-ALG-ER-P-Y10-03NZC26-P4-ALG-ER-K-Y10-05
Resources
- CorbettMaths - Solving Quadratics by FactorisingQuestions PDF · Answers
Terminology
- null factor law
- factorised form
- factor
- product
- solve
- coefficient
- extraneous solution
Task goals
- Foundation: Solve two-factor equations of the form $(x-a)(x-b)=0$ by applying the null factor law directly.
- Proficient: Solve equations with three factors, a repeated factor, or a leading coefficient inside one bracket, e.g. $(2x-1)(x+4)=0$ or $x(x-5)(x+2)=0$.
- Excellence: Rearrange non-zero-product equations into factorised = 0 form first (e.g. moving all terms to one side) before applying the null factor law, including checking for extraneous or repeated solutions.
Where this fits
What leads into this objective, and where it goes next.
Before
Simplifying and Solving with Algebraic Fractions
Solving Equations with Algebraic Fractions (Rational Equations)
Solving equations with variables on both sides
You are here
Solving Factorised Equations (Null Factor Law)
Do
Solving quadratic equations that are factorised or of the form x^2 + c = 0 (where c is an integer), and connecting the solutions to the x-intercepts of the related graph
Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y10-03
Know
The zero product property states that if two expressions multiply to be zero, then at least one expression must be zero (e.g. if ab = 0 then either a or b is 0, or if (x − a)(x − b) = 0 then either (x − a) = 0 or (x − b) = 0).
Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-K-Y10-05
Also under NA5-7:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.