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Factorising to solve quadratic equations of the form $ax^2+bx+c=0$

Algebra · Grade 4–6

Strand: Algebra Substrand: Solving quadratic equations Sparx code: U960 Sparx levels: 3, 4, 5 Tier: Higher Only

Key steps (method)

  • Remove brackets carefully (multiply each term inside by the factor outside).
  • If there are two brackets, use a systematic method (grid/FOIL) to multiply every term.
  • Collect like terms (same letters with same powers).
  • If factorising: take out the highest common factor first, then look for special patterns (difference of two squares, perfect square, etc.).
  • Quick check by expanding your factorised answer to see if you get back to the original.

Common mistakes

  • Forgetting to multiply every term when expanding brackets.
  • Sign errors, especially with negatives (e.g. −3(2x−5)).
  • Combining unlike terms (e.g. 2x + 3x^2).
  • Factorising only partially (missing a common factor).

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Factorising to solve quadratic equations of the form $ax^2+bx+c=0$ (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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Notes