IGCSE Factorisation: Complete Guide for Cambridge IGCSE Mathematics

IGCSE factorisation is a fundamental algebra skill in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering factoring algebraic expressions, common factors, and quadratic factorization is essential for solving equations and simplifying expressions.

This comprehensive IGCSE factorisation guide covers everything you need to know, including factoring by common factors, factoring quadratics, difference of two squares, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to factor expressions by common factors, factor quadratics, recognize special factorizations, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Algebra practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Factorisation Matters

IGCSE factorisation is an essential algebra skill. Here’s why it’s so important:

• High frequency topic: Factorization questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for solving quadratic equations and simplifying expressions
• Exam weight: Typically worth 3-6 marks per paper
• Real-world applications: Used in solving equations and simplifying complex expressions
• Problem-solving skills: Develops algebraic thinking and pattern recognition

Key insight from examiners: Students often struggle with recognizing factorable patterns or make errors when factoring quadratics. This guide will help you master these systematically.

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Understanding Factorisation

Factorisation means writing an expression as a product of factors. It’s the reverse of expanding brackets.

Expanding: 3(x + 2) = 3x + 6 Factorising: 3x + 6 = 3(x + 2)

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Factorising by Common Factors

Find the Highest Common Factor (HCF) and factor it out.

Step-by-Step Method

1. Find the HCF of all terms
2. Write the HCF outside brackets
3. Divide each term by the HCF
4. Write the result inside brackets

Worked Examples

Example 1: Factorise 6x + 12

Solution:

• HCF of 6 and 12 is 6
• 6x + 12 = 6(x + 2)

Answer: 6(x + 2)

Example 2: Factorise 4x² - 8x

Solution:

• HCF of 4x² and 8x is 4x
• 4x² - 8x = 4x(x - 2)

Answer: 4x(x - 2)

Example 3: Factorise 3xy + 6x

Solution:

• HCF of 3xy and 6x is 3x
• 3xy + 6x = 3x(y + 2)

Answer: 3x(y + 2)

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Factorising Quadratics

Quadratic expressions have the form ax² + bx + c.

Method 1: When a = 1

For x² + bx + c, find two numbers that:

• Add to give b
• Multiply to give c

Example: Factorise x² + 5x + 6

Solution:

• Need two numbers that add to 5 and multiply to 6
• Numbers: 2 and 3 (2 + 3 = 5, 2 × 3 = 6)
• x² + 5x + 6 = (x + 2)(x + 3)

Answer: (x + 2)(x + 3)

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Method 2: When a ≠ 1

Use the “ac method” or trial and error.

Example: Factorise 2x² + 7x + 3

Solution:

• Find two numbers that multiply to give ac = 2 × 3 = 6 and add to give b = 7
• Numbers: 6 and 1 (6 + 1 = 7, 6 × 1 = 6)
• 2x² + 7x + 3 = (2x + 1)(x + 3)

Answer: (2x + 1)(x + 3)

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Difference of Two Squares

Formula: a² - b² = (a + b)(a - b)

Example: Factorise x² - 9

Solution:

• x² - 9 = x² - 3²
• Using formula: (x + 3)(x - 3)

Answer: (x + 3)(x - 3)

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Common Examiner Traps

• Missing common factors - Always check for common factors first
• Sign errors - Watch positive/negative signs carefully
• Incomplete factorization - Continue until you can’t factor further
• Wrong pattern recognition - Learn to recognize different factorization patterns

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Practice Questions

Question 1

Factorise 5x + 15

Solution: HCF is 5: 5x + 15 = 5(x + 3)

Answer: 5(x + 3)

Question 2

Factorise x² - 5x + 6

Solution: Need numbers that add to -5 and multiply to 6: -2 and -3 x² - 5x + 6 = (x - 2)(x - 3)

Answer: (x - 2)(x - 3)

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Tutopiya Advantage: Personalised IGCSE Factorisation Coaching

• Live whiteboard walkthroughs of factorization problems
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Frequently Asked Questions About IGCSE Factorisation

What is factorisation?

Factorisation means writing an expression as a product of factors. It’s the reverse of expanding brackets.

How do I find common factors?

Find the Highest Common Factor (HCF) of all terms in the expression and factor it out.

How do I factorise quadratics?

For x² + bx + c, find two numbers that add to b and multiply to c.

What is the difference of two squares?

a² - b² = (a + b)(a - b) - a special factorization pattern.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Simplifying Algebraic Expressions: Complete Guide - Master algebraic simplification
• IGCSE Quadratic Equations: Complete Guide - Master solving quadratics
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Factorisation with Tutopiya

Ready to excel in IGCSE factorisation? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
• Interactive whiteboard sessions for visual learning
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• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master factorisation and achieve your target grade.

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