IGCSE Practice

IGCSE Algebra — Factorization Practice Extended

7 Cambridge IGCSE 0580 questions on factorization at the Extended tier — each with its full mark scheme. For the Core tier on the same skill, click here.

How to approach factorization — open the study guide

How to factorise on IGCSE 0580

Factorisation is one of the highest-frequency algebra skills on Cambridge IGCSE 0580. It shows up directly as "Factorise completely…" and indirectly as a step inside larger algebra and quadratic-equation problems.

Four patterns you must recognise on sight

  • Common factor: 6x + 9 = 3(2x + 3). Always check first.
  • Difference of two squares: a² − b² = (a − b)(a + b).
  • Quadratic trinomial: x² + bx + c = (x + p)(x + q) where p + q = b and p × q = c.
  • Grouping (4 terms): pair up, factor each pair, then take out the common bracket.

Common mark losses

  • Stopping at "incomplete" factorising — the question says "completely". Check every bracket.
  • Sign errors when factorising with a leading minus.
  • Missing the difference of two squares because the squares aren't obvious (4x² − 25 = (2x − 5)(2x + 5)).

Practice exercises

Exercise 1 — Cambridge IGCSE 0580 Mar 2025 Paper 42 Q18

Cambridge past paper 5 marks Paper 42 Mar 2025
IGCSE 0580 Mar 2025 Paper 42 Question 18 — Factorization (Extended, 5 marks)
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Mark scheme for IGCSE 0580 Mar 2025 Paper 42 Q18

Exercise 2 — Cambridge IGCSE 0580 Nov 2025 Paper 23 Q15

Cambridge past paper 4 marks Paper 23 Nov 2025
IGCSE 0580 Nov 2025 Paper 23 Question 15 — Factorization (Extended, 4 marks)
Show mark scheme
Mark scheme for IGCSE 0580 Nov 2025 Paper 23 Q15

Exercise 3 — Cambridge IGCSE 0580 Jun 2025 Paper 43 Q8

Cambridge past paper 4 marks Paper 43 Jun 2025
IGCSE 0580 Jun 2025 Paper 43 Question 8 — Factorization (Extended, 4 marks)
Show mark scheme
Mark scheme for IGCSE 0580 Jun 2025 Paper 43 Q8

Exercise 4 — Cambridge IGCSE 0580 Nov 2025 Paper 22 Q15

Cambridge past paper 3 marks Paper 22 Nov 2025
IGCSE 0580 Nov 2025 Paper 22 Question 15 — Factorization (Extended, 3 marks)
Show mark scheme
Mark scheme for IGCSE 0580 Nov 2025 Paper 22 Q15

Exercise 5 — Cambridge IGCSE 0580 Specimen 2025 Paper 41 Q10

Cambridge past paper 2 marks Paper 41 Specimen 2025
IGCSE 0580 Specimen 2025 Paper 41 Question 10 — Factorization (Extended, 2 marks)
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Mark scheme for IGCSE 0580 Specimen 2025 Paper 41 Q10

Exercise 6 — Cambridge IGCSE 0580 Jun 2025 Paper 42 Q14

Cambridge past paper 2 marks Paper 42 Jun 2025
IGCSE 0580 Jun 2025 Paper 42 Question 14 — Factorization (Extended, 2 marks)
Show mark scheme
Mark scheme for IGCSE 0580 Jun 2025 Paper 42 Q14

Exercise 7 — Cambridge IGCSE 0580 Mar 2024 Paper 42 Q5

Cambridge past paper 20 marks Paper 42 Mar 2024
IGCSE 0580 Mar 2024 Paper 42 Question 5 — Factorization (Extended, 20 marks)
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Mark scheme for IGCSE 0580 Mar 2024 Paper 42 Q5

Other Algebra subtopics