0580/23 Oct/Nov 2025, Question 15: Factorising Quadratic Expressions
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Factorise two algebraic expressions: a quadratic with three terms, and a four-term expression requiring grouping.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Factorise x² − 7x + 12 into two brackets.
- 1Two numbers that multiply to 12 and add to −7: −3 and −4
- 2x² − 7x + 12 = (x − 3)(x − 4)
Answer(x − 3)(x − 4)
Part (b) · 2 marks
Factorise 5x + 10y + 6ny + 3nx by grouping the terms.
- 15x + 10y + 3nx + 6ny = 5(x + 2y) + 3n(x + 2y)
- 2= (5 + 3n)(x + 2y)
Answer(5 + 3n)(x + 2y)
Stuck on a step? Read the free lesson: Factorising Quadratic Expressions
Practise more factorising quadratic expressions questions
Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on factorising quadratic expressions
Also searched as: 0580/23/O/N/25 · 0580_w25_qp_23 · 0580 w25 23 · question 15.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.