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# NCERT Solutions for Class 8 Maths Chapter 12 Factorisation - PDF Download `

NCERT solutions for class 8 maths chapter 12 Factorisation provides a comprehensive overview of all the topics and subtopics associated with factorization and their applications. The process of learning to factorize expressions is intricate and necessitates an in-depth comprehension of factors and procedures for enumerating them. With a lot of practice, you'll be able to quickly pick up all the knowledge you need to get ready for exams with the help of NCERT solutions class 8 maths chapter 12 provided by eSaral.

These NCERT solutions provide an organized and competent resource to establish a solid mathematical foundation. With the comprehensive training of all the questions included in these solutions, you can easily discover novel approaches to learning this topic. The variety of questions included in NCERT solutions for class 8 mathematics chapter 12 will enhance your problem-solving abilities.

eSaral’s NCERT solutions for class 8 maths chapter 12 provides students with a platform to expand their knowledge and gain mastery of the chapter. Each concept is presented in a stepwise format with numerous questions. In order to revise the entire chapter of class 8 maths chapter 12 and achieve high marks in the examinations, it is recommended to download the NCERT solution PDF. These solutions are also available for free to download on the official website of eSaral.

## Important Topics covered in Chapter 12 - Factorisation

NCERT solutions for class 8 maths chapter 12 covers all the main topics of factorization. Here, we will discuss all the topics included in chapter 12.

 12.1 Introduction 12.1.1 Factors of natural numbers 12.1.2 Factors of algebraic expressions 12.2 What is Factorisation ? 12.2.1 Method of common factors 12.2.2 Factorisation by regrouping terms 12.2.3 Factorisation using identities 12.2.4 Factors of the form (x + a) (x + b) 12.3 Division of Algebraic Expressions 12.3.1 Division of a monomial by another monomial 12.3.2 Division of a polynomial by a monomial 12.4 Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)

12.1 Introduction - In this section, you will learn about the factorisation of natural numbers and algebraic expressions.

12.1.1 Factors of natural numbers

12.1.2 Factors of algebraic expressions

You have learned about natural numbers in your previous classes. Now, you are going to learn how to factorize a natural number into prime factors. For example, if we have a natural number 45, then its prime factor is 3 * 3 * 5.

In your previous classes, you have already learned about Algebraic Expressions. Now, you are going to learn how to factorise an Algebraic expression into the prime factor. For example, if we have an algebraic expression 3xy, its prime factor is 3 * x * y

12.2 What is Factorisation ? - When we factorise an algebraic expression, This makes it easy to understand the expression as a product of its factors. These factors are natural numbers, Algebraic variables or Algebraic expressions.

For example, 2xy, 5x^3y, and 5x(y+2) are factorised forms.

In the following examples, the expression (2x + 4) and the expression (5x^2 + 9) are not in factorised form. To transform the expression in the form of a factor, we are going to use the following methods:

12.2.1 Method of common factors

12.2.2 Factorisation by regrouping terms

Regrouping -  We will rearrange the algebraic expression (Ex. 3xy+2+3+2ab), which will allow us to form the group (ex. 3xy+3+2ab+2), leading to factorisation.

12.2.3 Factorisation using identities

12.2.4 Factors of the form (x + a) (x + b)

The above-mentioned methods will explain how to factorize any natural numbers or algebraic expressions.

12.3 Division of Algebraic Expressions - Division, as mentioned in previous chapters, is the inverse operation of multiplication. For example, 5*6=30 gives 30÷5=6 or 30÷6=5.

12.3.1 Division of a monomial by another monomial -Here, you will learn to divide a monomial by another monomial.

For example, To divide 6x^2 to 2x,

Step1 -  factorise the monomial 2*3*x*x and 2*x

Step2 -  cancel the matched factor by their denominator

(2*3*x*x ÷ 2*x) = 3*x

12.3.2 Division of a polynomial by a monomial - Here, you will learn to divide a polynomial by a monomial.

For example, divide 6x^2(2x + y) by 2x

Step1: factorise the polynomial and monomial 2*3*x*x*(2*x + y) and 2*x

Step2: cancel the matched factor by their denominator

[2*3*x*x*(2*x + y) ÷ 2*x] = 3*x(2x + y)

12.4  Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial) - This section will teach you to divide the polynomial by the polynomial.

For example, To divide (7y^2 + 14x) to (y + 2)

Step1: factorise the polynomial and polynomial

7*y*y + 7*2*y and (y + 2)

7*y(y +2) and (y + 2)

Step2: cancel the matched factor by their denominator

[7*y(y +2) ÷ (y + 2)] = 7*y

Questions related to the Division of Polynomials begin to become more difficult in this chapter. You can access a large number of questions and solve them by referring to our NCERT solutions for class 8 maths chapter 12. Students can solve various questions ranging from low to high levels of difficulty in our study material. Solving these questions will help students to overcome their doubts and gain confidence in this chapter.

## NCERT Solutions for Class 8 Maths Chapter 12 Exercises

NCERT solution for class 8 maths chapter 12 Factorisation is designed by the mathematics expert team of eSaral. Students will get detailed NCERT solutions for every exercise in this chapter. This will help them to learn and test their problems while practicing. Students can get NCERT solutions for class 8 math chapter 12 from eSaral website.

Click on the below link to view exercise specific questions and NCERT solutions for class 8 math chapter 12.

 Exercise 12.1 3 Questions & Solutions Exercise 12.2 5 Questions & Solutions Exercise 12.3 5 Questions & Solutions

The NCERT solutions play an important role in helping students understand complex concepts. There are many chapters in class 8 that are difficult for students to understand. One of those chapters is chapter 12 Factorisation. Here, we are going to explore the benefits of downloading the NCERT solutions for class 8 math chapter 12  factorisation.

1. NCERT solutions for class 8 maths chapter 12 All exercise questions have been put together by our subject experts and are available for practice.

2. You can download our NCERT solutions for free in PDF format so you can practice all the questions included in the chapter.

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