Factorising for IGCSE Maths
Writing expressions as products of factors including common factors and trinomials. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Un
What You Need to Know
Writing expressions as products of factors including common factors and trinomials. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding factorising is essential for achieving a strong grade in your IGCSE Maths exam.
Understanding Factorising
Factorising is the reverse of expanding. The main types in IGCSE 0580 are: (1) common factor — take out the HCF, (2) difference of two squares — a² − b² = (a+b)(a−b), (3) trinomials — x² + bx + c = (x+p)(x+q) where p+q=b and p×q=c, and (4) grouping — for four-term expressions. Factorising completely means factorising until no further factorisation is possible. It is essential for solving quadratic equations.
Step-by-Step Method
- 1
Check for a common factor first
Always look for an HCF before any other method. 6x² + 9x = 3x(2x + 3). If there is a common factor, take it out first.
- 2
Recognise difference of two squares
a² − b² = (a+b)(a−b). Spot it: two perfect squares, minus sign between them. 4x² − 25 = (2x+5)(2x−5).
- 3
Factorise trinomials (a=1)
For x² + bx + c, find two numbers that add to b and multiply to c. For x² + 5x + 6: 2 and 3 (2+3=5, 2×3=6), so (x+2)(x+3).
- 4
Factorise trinomials (a≠1)
For ax² + bx + c, multiply a×c, find two numbers that add to b and multiply to ac, then split the middle term and factorise by grouping.
- 5
Factorise by grouping (4 terms)
Group into pairs, factorise each pair, then take out the common bracket: ax + ay + bx + by = a(x+y) + b(x+y) = (a+b)(x+y).
Worked Example
Question
Factorise completely: (a) x² − 7x + 12 (b) 2x² + 5x − 3
Solution
Part (a): x² − 7x + 12 Find two numbers: add to −7, multiply to +12 → −3 and −4. (x − 3)(x − 4) Part (b): 2x² + 5x − 3 a×c = 2×(−3) = −6. Find two numbers: add to 5, multiply to −6 → +6 and −1. Split middle term: 2x² + 6x − x − 3 Group: 2x(x + 3) − 1(x + 3) = (2x − 1)(x + 3) Answers: (a) (x−3)(x−4) (b) (2x−1)(x+3)
Exam Tips for Factorising
- Always check for a common factor first — if you miss it, you'll lose the 'completely' mark.
- After factorising, expand your answer mentally to verify it gives back the original expression.
- Difference of two squares only works with a MINUS sign: x² + 25 does NOT factorise over integers.
- In a 3-mark factorising question, each bracket may be worth a mark — write both factors even if you're unsure.
Practice Questions
Q1: Factorise completely: 3x² − 12.
Show hint
Take out common factor 3 first: 3(x²−4). Then use difference of two squares: 3(x+2)(x−2).
Q2: Factorise: x² − 3x − 10.
Show hint
Find two numbers that add to −3 and multiply to −10: −5 and +2.
Q3: Factorise: 6x² − 7x − 3.
Show hint
a×c = −18. Find two numbers adding to −7, multiplying to −18: −9 and +2. Split and group.
Frequently Asked Questions
What is factorising in IGCSE Maths?
Writing expressions as products of factors including common factors and trinomials.
Is factorising in the Core or Extended syllabus?
Factorising is part of the Core and Extended syllabus for IGCSE Mathematics 0580.
How do I revise factorising effectively?
Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on factorising rather than trying to cover everything at once.
Need Help with Factorising?
Book a free trial class and get personalised support from Teacher Rig.
Book Free Trial WhatsApp MeMore on Algebra and Graphs
Related Subtopics
Explore More
Master Factorising with Expert Help
Book a free 60-minute trial class with Teacher Rig. Get personalised guidance on Algebra and Graphs and every other IGCSE Maths topic.