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A4bFactorising

Edexcel GCSE Maths (1MA1), Higher tier · Algebra

Practise Factorising. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

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Sample questions

Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.

Question 1Easy3 marks
(a) Factorise \(6a + 9\)[1]
(b) Factorise fully \(6a^{2} + 15a\)[2]
Show the answer and mark scheme
(a) Answer: \(3(2a + 3)\)
  • B1 for \(3(2a + 3)\)
(b) Answer: \(3a(2a + 5)\)
  • B2 for \(3a(2a + 5)\) (B1 for a correct partial factorisation, e.g. \(a(6a + 15)\) or \(3(2a^{2} + 5a)\))

Worked solution: The highest common factor of the terms is \(3a\), so \(6a^{2} + 15a = 3a(2a + 5)\)

Question 2Medium3 marks
(a) Factorise fully \(18mn + 3m^{3}n^{2}\)[2]
(b) Factorise \(b(b - 2) + 4(b - 2)\)[1]
Show the answer and mark scheme
(a) Answer: \(3mn(6 + m^{2}n)\)
  • B2 for \(3mn(6 + m^{2}n)\) (B1 for a correct factorisation that is not complete, e.g. \(3(6mn + m^{3}n^{2})\) or \(mn(18 + 3m^{2}n)\))

Worked solution: The highest common factor is \(3mn\), so \(18mn + 3m^{3}n^{2} = 3mn(6 + m^{2}n)\)

(b) Answer: \((b - 2)(b + 4)\)
  • B1 for \((b - 2)(b + 4)\)

Worked solution: \((b - 2)\) is a common factor: \(b(b - 2) + 4(b - 2) = (b - 2)(b + 4)\)

Question 3Hard2 marks
Factorise \(9p^2 - 12pq - 5q^2\)[2]
Show the answer and mark scheme
Answer: \((3p - 5q)(3p + q)\)
  • M1 for \((3p \pm 5q)(3p \pm q)\) or a correct split of the middle term
  • A1 for \((3p - 5q)(3p + q)\)

Worked solution: Split the middle term: \(9p^2 - 12pq - 5q^2 = 9p^2 + 3pq - 15pq - 5q^2 = (3p - 5q)(3p + q)\)

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