NCERT Solutions for Class 8 Mathematics Chapter 14 – Factorisation
Mathematics is a subject of great importance and plays a great role in our lives. It helps boost our problem-solving skills, thereby increasing students’ productivity. As a result, students should focus on making Mathematics their strong subject.
Factorisation Class 8 is connected with algebraic expressions covered in lower classes. Thus, students should know the basics of algebraic expressions. Some of the main topics covered in this chapter include factorisation, division of algebraic expressions, division of algebraic expressions in the case of polynomials and all the concepts related to framing equations in Algebra.
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In our NCERT Solutions for Class 8 Mathematics Chapter 14, we have included the basics of algebraic expressions and all topics and sub-topics related to this chapter. Our solutions are a comprehensive set of study resources, including chapter notes, important questions and their answers, revision notes, etc. Students can confidently rely on our study resources and use them fully to learn the chapter and prepare for their exams. All our study materials are specially designed by keeping in mind the needs of every student.
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Key Topics Covered In NCERT Solutions for Class 8 Mathematics Chapter 14
You have already learnt in lower classes about the role of algebraic expressions in Mathematics. In this chapter, you will learn more about the factorisation of algebraic expressions, their division, and division in the case of polynomials which is one of the most important topics of this chapter. To score well in this chapter, students should primarily focus on the division of polynomials and should try to get a conceptual understanding of this topic properly.
Students can find a variety of questions based on the division of polynomials in our NCERT Solutions for Class 8 Mathematics Chapter 14. The different sets of questions will give students the confidence to easily solve the questions they would be facing in their school and competitive examinations.
By regularly practising and studying from our NCERT solutions, students are likely to develop a keen interest in the subject of Mathematics, which will help them easily ace their exams.
Introduction
In this section, we will learn about the factorisation of natural numbers and algebraic expressions.
We have learnt in our earlier classes about natural numbers. We will learn how to factorise a natural number into prime factors.
For example, if we have a natural number 30, then its prime factor is 2 * 3 * 5.
We already learnt about algebraic expressions in our earlier classes. We will learn how to factorise an algebraic expression into the prime factor.
For example, if we have an algebraic expression 5xy, its prime factor is 5 * x * y
What is factorisation?
When we factorise an algebraic expression, it simplifies the expression as a product of its factors. These factors are in the form of natural numbers, algebraic variables or algebraic expressions.
For example, 2xy, 5x^3y, and 5x(y+2) are factorised forms.
In other examples, the expressions; (2x+4) and 5x^2+9 are not in a factorised form. To change in factor form, we will use some methods given below:
Method1: method of common factors
Method2: 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.
Method3: factorisations using identities
Method4: factors of the form (x+a)(x+b)
The methods given above will clarify how to factorise any natural number or algebraic expressions. To learn each method’s step-by-step process, please visit our Extramarks website and refer to our NCERT Solutions for Class 8 Mathematics Chapter 14.
Division of algebraic expressions
As we learned in the earlier chapters, division is the inverse operation of multiplication.
For example, 5*6=30 gives 30÷5=6 or 30÷6=5.
Division of a monomial by another monomial
In this section, we 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
Division of a polynomial by a monomial
Here, we 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)
Learning how to do division of polynomials is a crucial topic that will be required in advanced algebraic equations. Our Mathematics experts have explained the division of a monomial and polynomial by another monomial with many solved examples in our NCERT Solutions for Class 8 Mathematics Chapter 14. Students can register on our website and get access to these NCERT solutions.
Division of algebraic expressions continued (polynomial ÷ polynomial)
This section will teach us 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
The questions related to the division of polynomials start getting harder in this section. Students can refer to our NCERT Solutions for Class 8 Mathematics Chapter 14 to get access to a lot of questions and their solved answers. A variety of questions with low to high difficulty levels are covered in our study materials. Solving them will help students clear their doubts and increase their confidence in this chapter.
Can you find the error?
In this section, we are provided with some examples to find the error in solving different division problems. Students can register on the Extramarks website and get access to our NCERT Solutions for Class 8 Mathematics Chapter 14 to learn from study notes for this section.
NCERT Exemplar Class 8 Mathematics
NCERT exemplar covers all NCERT-related questions. The subject matter experts design it, so students trust this book during their exam preparation. It covers all the core concepts related to the chapter and formulated questions according to it. As a result, no topic of the students remains untouched.
The book has all ranges of questions right from basics to advanced, which helps in gradually building the mindset of the students, due to which they start solving a variety of questions with ease.
NCERT Exemplar Class 8 Mathematics is available on the Extramarks website. Students can register on our website and get access to our study materials anytime. Students also learn how to manage their time efficiently during the examinations and study smartly once they refer to the NCERT Exemplar. The book develops not only the academic performance of the students but also all other aspects related to it.
Key Features of NCERT Solutions for Class 8 Mathematics Chapter 14
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Students who know how to study smartly are always top performers. Lakhs of students have registered for Extramarks online learning solutions and scored above-average marks in their exams.
Academic experts smartly design our NCERT Solutions for Class 8 Mathematics Chapter 14 to make learning easy and fun for students. Some of the key features of our study solutions are:
You will find all the important topics highlighted so that students know what topics to focus on the most during the preparation.
The NCERT solutions also have quick notes, mind maps, memorising techniques and tables for students to quickly learn every bit of the chapter.
After completing the NCERT Solutions for Class 8 Mathematics Chapter 14, students will understand all the aspects related to the factorisation of all algebraic expressions and will easily be able to apply in their higher classes too.
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