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Factorisation

ICSE · Class 9 · Mathematics

Summary of Factorisation for ICSE Class 9 Mathematics. Key concepts, important points, and chapter overview.

44 questions24 flashcards5 concepts

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A visual representation showing a polynomial being expressed as a product of its factors, illustrating that factorisation is the reverse of multiplication.
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Overview

Factorisation is the process of expressing a polynomial as a product of two or more simpler expressions called factors. It is the reverse of multiplication and is fundamental to solving algebraic equations, simplifying expressions, and understanding mathematical relationships. When we factorise x² +

Key Concepts

Find the Highest Common Factor (HCF)

Find the Highest Common Factor (HCF) of all terms and take it outside brackets. For example: 6a² - 3ax = 3a(2a - x), where 3a is the common factor.

Group terms with common factors

Group terms with common factors and factorise each group separately. Example: ab + bc + ax + cx = b(a + c) + x(a + c) = (a + c)(b + x).

For trinomials ax² + bx +

For trinomials ax² + bx + c, split the middle term coefficient 'b' into two parts whose sum is 'b' and product is 'ac'. Example: x² + 5x + 6 = x² + 3x

Uses the identity a²

Uses the identity a² - b² = (a + b)(a - b). Example: x² - 25 = x² - 5² = (x + 5)(x - 5). Can be extended to more complex forms.

Uses identities

Uses identities: a³ + b³ = (a + b)(a² - ab + b²) and a³ - b³ = (a - b)(a² + ab + b²). Example: 8a³ - 27b³ = (2a)³ - (3b)³ = (2a - 3b)(4a² + 6ab + 9b²)

Learning Objectives

  • Understand the concept of factorisation as the reverse of multiplication
  • Master different methods of factorisation including common factors, grouping, and splitting middle terms
  • Factorise trinomials of the form ax² + bx + c using systematic approaches
  • Apply difference of squares formula: a² - b² = (a + b)(a - b)
  • Factorise sum and difference of cubes using standard identities

Frequently Asked Questions

What are the important topics in Factorisation for ICSE Class 9 Mathematics?
Factorisation covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Factorisation — ICSE Class 9 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All 28 chapters — ICSE Class 9 Mathematics Chapter Summary

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