Solving Cubic Equations

Solve cubic equations already given in fully factorised form using the null factor law.

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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

Terminology

  • factor theorem
  • polynomial division
  • quotient
  • remainder
  • null factor law
  • repeated root
  • irrational root
  • cubic equation

Task goals

  • Foundation: Solve cubic equations already given in fully factorised form using the null factor law.
  • Proficient: Apply the factor theorem to identify one linear factor of a cubic, divide to obtain a quadratic factor, and solve to find all roots.
  • Excellence: Solve cubics with repeated or irrational roots and interpret the solutions in a graphical or applied context, such as identifying turning points or intersection points.

Where this fits

What leads into this objective, and where it goes next.

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Solving Cubic Equations

Solving Cubic Equations

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