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!!!