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 - 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.

Benefits of Downloading The NCERT Solutions for Class 8 Maths Chapter 12 - Factorisation

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.

3. You'll get accurate, step-wise answers to your questions with our NCERT solutions, written by subject specialists.

4. The eSaral math NCERT solutions are well-structured and comprehensible for you to understand the topics and concepts properly.

Frequently Asked Questions

Question 1. What do you understand by factorisation according to NCERT solutions for class 8 maths chapter 12 ?

Answer 1. Factorization is the division of a number into smaller numbers that, when multiplied together, form the original number. In simplest terms, factorisation of an algebraic expression is the writing of the expression as the product of the factors. The factors can be numbers, algebraic variables, or algebras.

Question 2. Why is NCERT solutions chapter 12 Factorization so important in class 8 maths ?

Answer 2. NCERT solutions for class 8 maths Chapter 12 factorization are high-quality resources designed by our mathematics experts for students to learn maths. With consistent practice of questions and examples in these solutions, students can achieve conceptual fluency and correct problem-solving approaches needed for this chapter. With easy-to-follow steps  in these solutions, it’s easy for students to understand complex questions and solutions.