NCERT Class 8 Mathematics Mathematics: Chapter 12 — Factorisation
This chapter introduces the concept of factorisation in mathematics, building upon the understanding of factors of natural numbers from Class VI. It explains how algebraic expressions can be broken down into their irreducible factors, similar to prime factors of numbers. The chapter details the 'method of common factors' for factorising expressions. It demonstrates how to identify common factors in terms of numbers, variables, and algebraic expressions, and then use the distributive law to rewrite the expression as a product of these factors. Examples like 2x + 4 = 2(x + 2) and 5xy + 10x = 5x(y + 2) are used to illustrate the process. This foundational understanding is crucial for further algebraic manipulations and problem-solving in CBSE mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 12 — Factorisation |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 5 minutes |
| Word count | 861 |
Learning outcomes
- Understand the concept of factors for natural numbers and algebraic expressions.
- Identify irreducible factors of algebraic terms.
- Apply the method of common factors to factorise algebraic expressions.
- Utilise the distributive law in factorisation.
- Rewrite expressions as a product of their irreducible factors.
Vocabulary
| Word | Meaning |
|---|---|
| Factor | A number or algebraic expression that divides another number or expression without a remainder. |
| Prime factor | A factor that is a prime number. |
| Irreducible factor | A factor that cannot be further expressed as a product of factors (analogous to prime factors in algebra). |
| Factorisation | The process of writing an algebraic expression as a product of its factors. |
| Distributive law | A property that states a(b + c) = ab + ac. |
| Common factor | A factor that is shared by two or more terms or expressions. |
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Practice questions
- Write the prime factor form of 70. Answer: 70 = 2 × 5 × 7
- Identify the irreducible factors of 5xy. Answer: 5, x, and y
- Factorise the expression 2x + 4. Answer: 2(x + 2)
- Factorise the expression 5xy + 10x. Answer: 5x(y + 2)
Frequently asked questions
What is factorisation in mathematics?
Factorisation is the process of writing an algebraic expression as a product of its factors, which can be numbers, variables, or other algebraic expressions.
What are irreducible factors in algebraic expressions?
Irreducible factors are factors of an algebraic expression that cannot be further broken down into a product of simpler factors, similar to prime numbers for natural numbers.
How is the distributive law used in factorisation?
The distributive law (a(b + c) = ab + ac) is used in reverse to factorise expressions. For example, ab + ac can be written as a(b + c) by taking out the common factor 'a'.
What is the method of common factors?
The method of common factors involves identifying the factors that are common to all terms in an expression and then factoring them out using the distributive law.
Is 1 considered a factor when factorising algebraic expressions?
Similar to natural numbers, 1 is a factor of every term, but it is usually not shown as a separate factor unless specifically required.
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NCERT Class 8 Mathematics — Mathematics — Chapter 12 — Factorisation. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.