NCERT Solutions for Class 8 Maths Chapter 14 Factorization

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 factors.

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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 NCERT solutions for Class 8 Maths chapter 14 Factorization. CheckNCERT Solutions from Classes 6 to 12 to learn Science and Maths. Here you will get the detailed NCERT Solutions for Class 8 by clicking on the link.

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NCERT Solutions for Class 8 Maths Chapter 14 Factorization For All Exercises-

NCERT Solutions for Class 8 Maths Chapter 14 Factorization Topic 14.2.1 Method Of Common Factor

Question:(i) Factorise:

Answer:

We have



So, we have common in both
Therefore,

Question:(ii) Factorise : 22y-32z

Answer:

We have,


So, we have 11 common in both
Therefore,

Question:(iii) Factorise :

Answer:

We have


So, we have

common in both
Therefore,

NCERT Solutions for Class 8 Maths Chapter 14 Factorization-Exercise: 14.1

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

Answer:

We have


So, the common factors between the two are

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

Answer:

We have,


Therefore, the common factor between these two is 2y

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

Answer:

We have,


Therefore, the common factor is

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

Answer:

We have,



Therefore, the common factor between these three is 1

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

Answer:

We have,



Therefore, the common factors is

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

Answer:

We have,



Therefore, the common factors is

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

Answer:

We have,



Therefore, the common factors between these three is

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

Answer:

We have,



Therefore, the common factors between these three are

Question:2(i) Factorise the following expressions

Answer:

We have,

Therefore, 7 is a common factor

Question:2(ii) Factorise the following expressions

Answer:

We have,


on factorization

Question:2(iii) Factorise the following expressions

Answer:

We have,



Question:2(iv) Factorise the following expressions

Answer:

We have,


on factorization we get,


Question:2(v) Factorise the following expressions

Answer:

We have,


on factorization we get,


Question:2(vi) Factorise the following expressions

Answer:

We have,


on factorization we get,


Question:2(vii) Factorise the following expressions

Answer:

We have,



on factorization we get,

Question:2(viii) Factorise the following expressions

Answer:

We have,



on factorization we get,


Question:2(ix) Factorise the following expressions

Answer:

We have,



Therefore, on factorization we get,


Question:2(x) Factorise the following expressions

Answer:

We have,



Therefore, on factorization we get,

Question:3(i) Factorise

Answer:

We have,




Therefore, on factorization we get,


Question:3(ii) Factorise

Answer:

We have,




Therefore, on factorization we get,


Question:3(iii) Factorise

Answer:

We have,


Therefore, on factorization we get,

Question:3(iv) Factorise

Answer:

We have,


Therefore, on factorization we get,

Question:3(v) Factorise

Answer:

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

Answer:

We have,



Therefore,

Question:1(ii) Factorise the following expressions

Answer:

We have,



Therefore,

Question:1(iii) Factorise the following expressions

Answer:

We have,



Therefore,

Question:1(iv) Factorise the following expressions

Answer:

We have,



Therefore,

Question:1(v) Factorise the following expressions

Answer:

We have,


Question:1(vi) Factorise the following expressions

Answer:

We have,



Therefore,

Question:1(vii) Factorise the following expressions

Answer:

We have,
=
=
=

Question:1(viii) Factorise the following expressions

Answer:

We have,
= + + +
= = =

Question:2(i) Factorise :

Answer:

This can be factorized as follows
=

Question:2(ii) Factorise the following expressions

Answer:

We have,


Question:2(iii) Factorise

Answer:

This can be factorised as follows
=

Question:2(iv) Factorise

Answer:

The given question can be factorised as follows

Question:2(v) Factorise

Answer:

We have,
(using )

Question:2(vi) Factorise

Answer:

We have,
= (using )

Question:2(vii) Factorise

Answer:

We have,
=

Question:2(viii) Factorise

Answer:

We have,
=
=
)

Question:3(i) Factorise the following expressions

Answer:

We have,


Therefore,


Question:3(ii) Factorise the following expressions

Answer:

We have,


Therefore,

Question:3(iii) Factorise the following expressions

Answer:

We have,



Therefore,


Question:3(iv) Factorise the following expressions

Answer:

We have,

Question:3(v) Factorise the following expressions

Answer:

We have,


Question:3(vi) Factorise the following expressions

Answer:

We have,

Take ( y+z) common from this
Therefore,

Question:3(vii) Factorise the following expressions

Answer:

We have,


Therefore,

Question:3(viii) Factorise

Answer:

We have,


Therefore,

Question:3(ix) Factorise the following expressions

Answer:

We have,


Therefore,

Question:4(i) Factorise

Answer:

We have,
=

Question:4(ii) Factorise

Answer:

We have,
=

Question:4(iii) Factorise

Answer:

We have,
=


Question:4(iv) Factorise

Answer:

We have,
=
=
=
=

Question:4(v) Factorise

Answer:

We have,
=
=
=
=
=
=

Question:5(i) Factorise the following expression

Answer:

We have,
=


Therefore,

Question:5(ii) Factorise the following expression

Answer:

We have,
=


Therefore,

Question:5(iii) Factorise the following expression

Answer:

We have,
=


Therefore,

NCERT Solutions for Class 8 Maths Chapter 14 Factorization Topic 14.3.1 Division Of A Monomial By Another Monomial

Question:(i) Divide

Answer:

We have,

Question:(ii) Divide

Answer:

We have,

NCERT Solutions for Class 8 Maths Chapter 14 Factorization-Exercise: 14.3

Question:1(i) Carry out the following divisions

Answer:

,

This is done using factorization.

Question:1(ii) Carry out the following divisions

Answer:

We have,


Therefore,

Question:1(iii) Carry out the following divisions

Answer:

We have,


Therefore,

Question:1(iv) Carry out the following divisions

Answer:

We have,

Question:1(v) Carry out the following divisions

Answer:

We have,

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

Answer:

We have,


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

Answer:

We have,

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

Answer:

We have,

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

Answer:

We have,


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

Answer:

We have,

Question:3(i) workout the following divisions

Answer:

We have,

Therefore,

Question:3(ii) workout the following divisions

Answer:

We have,

Therefore,

Question:3(iii) workout the following divisions

Answer:

We have,

Therefore,

Question:3(iv) workout the following divisions

Answer:

We have,


Question:3(v) workout the following divisions

Answer:

We have,


Therefore,

Question:4(i) Divide as directed

Answer:

We have,

Question:4(ii) Divide as directed

Answer:

We have,

Question:4(iii) Divide as directed

Answer:

We have,

Question:4(iv) Divide as directed

Answer:

We have,

Question:4(v) Divide as directed

Answer:

We have,

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

Answer:

We have,

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

Answer:

We have,

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

Answer:

We have,

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

Answer:

We first simplify our numerator
So,

Add and subtract 64




Now,

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

Answer:

We have,

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

Answer:

We first simplify our numerator,
( ) =

using

Now,

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

Answer:

We first simplify our numerator,
using
=
=
Now,

NCERT Solutions for Class 8 Maths Chapter 14 Factorization-Exercise: 14.4

Question:1 Find and correct the errors in the following mathematical statements

Answer:

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

Question:2 Find and correct the errors in the following mathematical statements

Answer:

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

Question:3 Find and correct the errors in the following mathematical statements

Answer:

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

Question:4 Find and correct the errors in the following mathematical statements

Answer:

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

Question:5 Find and correct the errors in the following mathematical statements

Answer:

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

Question:6 Find and correct the errors in the following mathematical statements

Answer:

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

Question:7 Find and correct the errors in the following mathematical statements

Answer:

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

Question:8 Find and correct the errors in the following mathematical statements

Answer:

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

Question:9 Find and correct the errors in the following mathematical statements

Answer:

LHS IS

using

RHS IS

Correct statement is

Question:10(a) Find and correct the errors in the following mathematical statements

Substituting in

Answer:

We need to substitute x = -3 in




so the given statement is wrong
Correct statement is

Question:10(b) find and correct the errors in the following mathematical statements

Substituiting x = -3 in

Answer:

We need to substitute x = -3 in


so the given statement is wrong
Correct statement is

Question:10(c) find and correct the errors in the following mathematical statements

Substituting x = - 3 in

Answer:

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

Question:11 Find and correct the errors in the following mathematical statements

Answer:

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

Correct statement is

=

Question:12 Find and correct the errors in the following mathematical statements

Answer:

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

=

Question:13 Find and correct the errors in the following mathematical statements.

Answer:

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

Question:14 Find and correct the errors in the following mathematical statements.

Answer:

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

Question:15 Find and correct the errors in the following mathematical statements.

Answer:

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

Question:16 Find and correct the errors in the following mathematical statements.

Answer:

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

Question:17 Find and correct the errors in the following mathematical statements.

Answer:

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

Question:18 find and correct the errors in the following mathematical statements.

Answer:

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,

Question:19 find and correct the errors in the following mathematical statements

Answer:

Our L.H.S. is R.H.S.

Correct statement is

Question:20 find and correct the errors in the following mathematical statements

Answer:

Our L.H.S. is R.H.S.

Correct statement is

Question:21 find and correct the errors in the following mathematical statements

Answer:

Our L.H.S. is R.H.S.

Correct statement is

Factorization Class 8 Math Chapter 14-Topics

  • What is Factorization?
  • Division of Algebraic Expressions
  • Division of Algebraic Expressions Continued(Polynomial divide; Polynomial)
  • Can you Find the Error?

NCERT Solutions for Class 8 Maths: Chapter-Wise

Chapter -1

Rational Numbers

Chapter -2

Linear Equations in One Variable

Chapter-3

Understanding Quadrilaterals

Chapter-4

Practical Geometry

Chapter-5

Data Handling

Chapter-6

Squares and Square Roots

Chapter-7

Cubes and Cube Roots

Chapter-8

Comparing Quantities

Chapter-9

Algebraic Expressions and Identities

Chapter-10

Visualizing Solid Shapes

Chapter-11

Mensuration

Chapter-12

Exponents and Powers

Chapter-13

Direct and Inverse Proportions

Chapter-14

Factorization

Chapter-15

Introduction to Graphs

Chapter-16

Playing with Numbers

NCERT Solutions for Class 8: Subject-Wise

  • NCERT Solutions for Class 8 Maths
  • NCERT Solutions for Class 8 Science

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 NCERT solutions for Class 8 Maths chapter 14 Factorizations, you will come across some applications like simplifying expressions and solving quadratic equations. Some important expressions from NCERT solutions for Class 8 Maths chapter 14 Factorizations are given below which you should remember.

Happy Reading!!!