# NCERT Solutions for Class 8 Maths Chapter 14 Factorization

NCERT Solutions for Class 8 Maths Chapter 14 Factorization: Decomposition of expression or mathematical object as a product of several factors is known as factorization. It is a process to factorize algebraic expressions and write this expression as a product of its factors. These are usually smaller or simpler objects of the same kind. It makes easy to multiply and find the least common multiple and greatest common factor. In NCERT solutions for class 8 maths chapter 14 factorization, you will be dealing with questions related to algebraic expressions and natural numbers. Important topics like methods of common factors, factorization using identities, factorization by regrouping terms, factors of the form (x + a) ( x + b) and division of algebraic expressions are covered in this chapter. There are 4 exercises with 34 questions given in the NCERT textbook. All these questions are prepared in the solutions of NCERT for class 8 maths chapter 14 factorization in a step-by-step manner. It will be easy for you to understand the concept. For a better understanding of the concept, there are some practice questions given after every topic. You will find solutions to these practice questions also in CBSE NCERT solutions for class 8 maths chapter 14 factorization. Check NCERT solutions from class 6 to 12 to learn science and maths.

## Important Topics of NCERT Class 8 Maths Chapter 14 Factorization:

• 14.1 Introduction
• 14.2 What is Factorization?
• 14.3 Division of Algebraic Expressions
• 14.4 Division of Algebraic Expressions Continued(Polynomial divide; Polynomial)
• 14.5 Can you Find the Error?

## Solutions of NCERT for class 8 maths chapter 14 factorization topic 14.2.1 method of common factor

Question:(i) Factorise:

We have

So, we have   common in both
Therefore,

Question:(ii) Factorise :  22y-32z

We have,

So, we have   11 common in both
Therefore,

Question:(iii) Factorise :

We have

So, we have

common in both
Therefore,

## Question:1(i) Find the common factors of the given terms.

We have

So, the common factors between the two are

Question:1(ii) Find the common factors of the given terms

We have,

Therefore, the common factor between these two is 2y

Question:1(iii) Find the common factors of the given terms

We have,

Therefore, the common factor is

Question:1(iv) Find the common factors of the given terms.

We have,

Therefore, the common factor between these three  is  1

Question:1(v) Find the common factors of the given terms

We have,

Therefore, the common factors is

Question:1(vi) Find the common factors of the given terms

We have,

Therefore, the common factors is

Question:1(vii) Find the common factors of the given terms

We have,

Therefore, the common factors between these three is

Question:1(viii) Find the common factors of the given terms

We have,

Therefore, the common factors between these three are

Question:2(i) Factorise the following expressions

We have,

Therefore,  7 is a common factor

Question:2(ii) Factorise the following expressions

We have,

on factorization

Question:2(iii) Factorise the following expressions

We have,

Question:2(iv) Factorise the following expressions

We have,

on factorization we get,

Question:2(v) Factorise the following expressions

We have,

on factorization we get,

Question:2(vi) Factorise the following expressions

We have,

on factorization we get,

Question:2(vii) Factorise the following expressions

We have,

on factorization we get,

Question:2(viii) Factorise the following expressions

We have,

on factorization we get,

Question:2(ix) Factorise the following expressions

We have,

Therefore,   on factorization we get,

Question:2(x) Factorise the following expressions

We have,

Therefore,    on factorization we get,

Question:3(i) Factorise

We have,

Therefore,   on factorization we get,

Question:3(ii) Factorise

We have,

Therefore, on factorization we get,

Question:3(iii) Factorise

We have,

Therefore, on factorization we get,

Question:3(iv) Factorise

We have,

Therefore, on factorization we get,

Question:3(v) Factorise

We have,

Therefore, on factorization we get,

NCERT solutions for class 8 maths chapter 14 factorization-Exercise: 14.2

Question:1(i) Factorise the following expressions

We have,

Therefore,

Question:1(ii) Factorise the following expressions

We have,

Therefore,

Question:1(iii) Factorise the following expressions

We have,

Therefore,

Question:1(iv) Factorise the following expressions

We have,

Therefore,

Question:1(v) Factorise the following expressions

We have,

Question:1(vi) Factorise the following expressions

We have,

Therefore,

Question:1(vii) Factorise the following expressions

We have,
=
=
=

Question:1(viii) Factorise the following expressions

We have,
=  +  +  +
= =  =

Question:2(i) Factorise :

This can be factorized as follows
=

Question:2(ii) Factorise the following expressions

We have,

Question:2(iii) Factorise

This can be factorised as follows
=

Question:2(iv) Factorise

The given question can be factorised as follows

Question:2(v) Factorise

We have,
(using   )

Question:2(vi) Factorise

We have,
=                 (using  )

Question:2(vii) Factorise

We have,
=

Question:2(viii) Factorise

We have,
=
=
)

Question:3(i) Factorise the following expressions

We have,

Therefore,

Question:3(ii) Factorise the following expressions

We have,

Therefore,

Question:3(iii) Factorise the following expressions

We have,

Therefore,

Question:3(iv) Factorise the following expressions

We have,

Question:3(v) Factorise the following expressions

We have,

Question:3(vi) Factorise the following expressions

We have,

Take ( y+z) common from this
Therefore,

Question:3(vii) Factorise the following expressions

We have,

Therefore,

Question:3(viii) Factorise

We have,

Therefore,

Question:3(ix) Factorise the following expressions

We have,

Therefore,

Question:4(i) Factorise

We have,
=

Question:4(ii) Factorise

We have,
=

Question:4(iii) Factorise

We have,
=

Question:4(iv) Factorise

We have,
=
=
=
=

Question:4(v) Factorise

We have,
=
=
=
=
=
=

Question:5(i) Factorise the following expression

We have,
=

Therefore,

Question:5(ii) Factorise the following expression

We have,
=

Therefore,

Question:5(iii) Factorise the following expression

We have,
=

Therefore,

## Solutions of NCERT for class 8 maths chapter 14 factorization topic 14.3.1 division of a monomial by another monomial

Question:(i) Divide

We have,

Question:(ii) Divide

We have,

## CBSE NCERT solutions for class 8 maths chapter 14 factorization-Exercise: 14.3

Question:1(i) Carry out the following divisions

,

This is done using factorization.

Question:1(ii) Carry out the following divisions

We have,

Therefore,

Question:1(iii) Carry out the following divisions

We have,

Therefore,

Question:1(iv) Carry out the following divisions

We have,

Question:1(v) Carry out the following divisions

We have,

Question:2(i) Divide the given polynomial by the given monomial

We have,

Question:2(ii) Divide the given polynomial by the given monomial

We have,

Question:2(iii) Divide the given polynomial by the given monomial

We have,

Question:2(iv) Divide the given polynomial by the given monomial

We have,

Question:2(v) Divide the given polynomial by the given monomial

We have,

Question:3(i) workout the following divisions

We have,

Therefore,

Question:3(ii) workout the following divisions

We have,

Therefore,

Question:3(iii) workout the following divisions

We have,

Therefore,

Question:3(iv) workout the following divisions

We have,

Question:3(v) workout the following divisions

We have,

Therefore,

Question:4(i) Divide as directed

We have,

Question:4(ii) Divide as directed

We have,

Question:4(iii) Divide as directed

We have,

Question:4(iv) Divide as directed

We have,

Question:4(v) Divide as directed

We have,

Question:5(i) Factorise the expression and divide then as directed

We have,

Question:5(ii) Factorise the expression and divide then as directed

We have,

Question:5(iii) Factorise the expression and divide then as directed

We have,

Question:5(iv) Factorise the expression and divide then as directed

We first simplify our numerator
So,

Now,

Question:5(v) Factorise the expression and divide then as directed

We have,

Question:5(vi) Factorise the expression and divide then as directed

We first simplify our numerator,
() =

using

Now,

Question:5(vii) Factorise the expression and divide then as directed

We first simplify our numerator,
using
=
=
Now,

## NCERT solutions for class 8 maths chapter 14 factorization-Exercise: 14.4

Our L.H.S.

R.H.S.
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is

Our  L.H.S.

R.H.S.=
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is

Our L.H.S.
R.H.S. =
It is clear from the above that L.H.S. is not equal to R.H.S.
SO, correct statement is

Our L.H.S.
R.H.S.
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is

Our L.H.S. is

R.H.S. = 0
IT is clear from the above that  L.H.S. is not equal to R.H.S.
So, Correct statement is

Our L.H.S. is

R.H.S. =
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is

Our L.H.S. is

R.H.S.
It is clear  from the above that L.H.S. is not equal to R.H.S.
So, correct statement is

Our L.H.S. is

R.H.S. = 9x
It is clear from the above that L.H.S. is not equal to R.H.S.
So, the correct  statement is

LHS IS

using

RHS IS

Correct statement is

We need to substitute  x = -3 in

so the given statement is wrong
Correct statement is

We need to substitute x = -3 in

so the given statement is wrong
Correct statement is

We need to  Substitute  x = - 3 in
=
= 9 - 15
= - 6     R.H.S
Correct statement is   Substitute  x = - 3 in      gives -6

Our L.H.S.  is
=            using
=   R.H.S.

Correct statement  is

=

Our L.H.S. is
=                                         using
=       R.H.S.
Correct statement  is

=

Our L.H.S. is  (2a + 3b)(a -b)
=
=       R.H.S.
Correct statement is  (2a + 3b)(a -b) =

Oue L.H.S. is  (a + 4)(a + 2)
=
=      R.H.S.
Correct statement is   (a + 4)(a + 2)  =

Our L.H.S. is (a - 2) (a - 4)
=
=     R.H.S.
Correct statement is  (a - 2) (a - 4)  =

Our L.H.S.  is

R.H.S. = 0
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement  is

Our L.H.S.  is

R.H.S. = 2
It is clear from the above stattement that L.H.S. is not equal to R.H.S.
So, correct statement is

Our L.H.S.

R.H.S. = 1/2

It can be clearly observed that L.H.S is not equal to R.H.S

So, the correct statement is,

Our L.H.S. is     R.H.S.

Correct statement is

Our L.H.S. is     R.H.S.

Correct statement is

Our L.H.S. is    R.H.S.

Correct statement is

## NCERT solutions for class 8 maths: Chapter-wise

 Chapter -1 NCERT solutions for class 8 maths chapter 1 Rational Numbers Chapter -2 Solutions of NCERT for class 8 maths chapter 2 Linear Equations in One Variable Chapter-3 CBSE NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals Chapter-4 NCERT solutions for class 8 maths chapter 4 Practical Geometry Chapter-5 Solutions of NCERT for class 8 maths chapter 5 Data Handling Chapter-6 CBSE NCERT solutions for class 8 maths chapter 6 Squares and Square Roots Chapter-7 NCERT solutions for class 8 maths chapter 7 Cubes and Cube Roots Chapter-8 Solutions of NCERT for class 8 maths chapter 8 Comparing Quantities Chapter-9 NCERT solutions for class 8 maths chapter 9 Algebraic Expressions and Identities Chapter-10 CBSE NCERT solutions for class 8 maths chapter 10 Visualizing Solid Shapes Chapter-11 NCERT solutions for class 8 maths chapter 11 Mensuration Chapter-12 Solutions of NCERT for class 8 maths chapter 12 Exponents and Powers Chapter-13 CBSE NCERT solutions for class 8 maths chapter 13 Direct and Inverse Proportions Chapter-14 NCERT solutions for class 8 maths chapter 14 Factorization Chapter-15 Solutions of NCERT for class 8 maths chapter 15 Introduction to Graphs Chapter-16 CBSE NCERT solutions for class 8 maths chapter 16 Playing with Numbers

## NCERT solutions for class 8: Subject-wise

Factorization is a key skill to solve a problem where you need to find the value of x. It will strengthen your foundations of algebra, trigonometry, calculus, and higher class maths. It has a lot of applications like calculation, make multiplication easy, prime factorization, finding LCM and HCF, ​​​​​solving polynomial equations, quadratic equations, and simplifying expression, etc. In solutions of NCERT for class 8 maths chapter 14 factorizations you will come across some applications like simplifying expressions and solving quadratic equations. Some important expressions from CBSE NCERT solutions for class 8 maths chapter 14 factorizations are given below which you should remember.