Factorising quadratics where a > 1

Factorise quadratics of the form ax^2 + bx + c where a is not 1, by taking out any common factor first and then splitting the middle term so the four resulting terms factorise in matching pairs.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Other: Not in Beta Textbook find other resource
  • CorbettMaths worksheet

Terminology

  • factorise
  • coefficient
  • common factor
  • quadratic expression

Task goals

  • Factorise quadratics ax^2+bx+c where a is not 1, with positive coefficients b and c.
  • Factorise quadratics ax^2+bx+c where a is not 1, with negative b and/or c.
  • Complete a partially factorised quadratic, or identify which of two given factorisations is correct.
  • Factorise harder quadratics with larger coefficients, including taking out a common factor first and factorising expressions with a negative leading coefficient.
  • Determine whether a given factorisation of a quadratic is correct and explain any error.
  • Solve a quadratic equation by factorising and setting each factor equal to zero.
  • Find an unknown coefficient in a quadratic given its factorised form, and expand or construct quadratics from given factors.