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Factorising questions and answers

Factorising is expanding in reverse: you write an expression as a product of factors. The questions go from taking out a common factor, through quadratics like x2+7x+12x^2 + 7x + 12 and the difference of two squares, to Higher-tier quadratics where the x2x^2 term has a number in front. Type your answer with brackets, for example (x+3)(x-2); the checker tells you if something can still be factorised further.

12 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .

Start the questions Factorising: the full guide Factorising calculator

Where factorising comes up

GCSE (AQA, Edexcel, OCR)Common factors and quadratics of the form x² + bx + c, including the difference of two squares: Foundation and Higher. ax² + bx + c: Higher only.
Cambridge IGCSE (0580)Common factors: Core and Extended. Quadratics, ax² + bx + c and a²x² − b²y²: Extended.
Edexcel International GCSE (4MA1)Common factors and simple quadratics: Foundation and Higher. Quadratics such as 6x² − 5x − 6: Higher.

The method

  1. Always look for a common factor first and take it outside a bracket.
  2. For x² + bx + c, find two numbers that multiply to c and add to b.
  3. For a² − b², use the difference of two squares: (a + b)(a − b).
  4. For ax² + bx + c (Higher), find two numbers that multiply to a × c and add to b, split the middle term, then factorise in pairs.
  5. Check by expanding your answer: you should get back to where you started.

Factorising questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Factorise 6x+96x + 9

Question 2Warm-upFoundation

Factorise fully 8x2−12x8x^2 - 12x

Question 3Warm-upFoundation

Factorise x2+7x+12x^2 + 7x + 12

Exam-style

Question 4Exam-styleFoundation

Factorise x2−2x−15x^2 - 2x - 15

Question 5Exam-styleFoundation

Factorise x2−49x^2 - 49

Question 6Exam-styleFoundation

Factorise x2+4xx^2 + 4x

Question 7Exam-styleFoundation

Factorise x2−3x−10x^2 - 3x - 10, and hence solve x2−3x−10=0x^2 - 3x - 10 = 0.

Question 8Exam-styleHigher

Factorise 2x2+7x+32x^2 + 7x + 3

Question 9Exam-styleHigher

Factorise 3x2−10x−83x^2 - 10x - 8

Question 10Exam-styleHigher

Factorise 6x2−x−26x^2 - x - 2

Challenge

Question 11ChallengeFoundation

Factorise fully 2x2−182x^2 - 18

Question 12ChallengeHigher

Factorise 4x2−25y24x^2 - 25y^2

Common mistakes

  • Not factorising fully: 2x(4x − 6) still has a common factor of 2.
  • Getting the signs the wrong way round: x² − 2x − 15 is (x − 5)(x + 3), not (x + 5)(x − 3).
  • Trying to factorise a sum of two squares like x² + 9, which doesn't factorise.
  • Forgetting to take out a common factor before using the difference of two squares: 2x² − 18 = 2(x + 3)(x − 3).

Stuck on one of these?

The TutorAura AI tutor works through it with you step by step, with the reason for each step, then gives you one like it to try. It checks your working too.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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