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NCERT solutions for Mathematics [English] Class 8 chapter 12 - Factorisation [Latest edition]

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Chapters

    1: Rational Numbers

    2: Linear Equations in One Variable

    3: Understanding Quadrilaterals

    4: Data Handling

    5: Squares and Square Roots

    6: Cubes and Cube Roots

    7: Comparing Quantities

    8: Algebraic Expressions and Identities

    9: Mensuration

    10: Exponents and Powers

    11: Direct and Inverse Proportions

▶ 12: Factorisation

    13: Introduction to Graphs

NCERT solutions for Mathematics [English] Class 8 chapter 12 - Factorisation - Shaalaa.com

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Solutions for Chapter 12: Factorisation

Below listed, you can find solutions for Chapter 12 of CBSE NCERT for Mathematics [English] Class 8.

EXERCISE 12.1EXERCISE 12.2EXERCISE 12.3

EXERCISE 12.1 [Pages 148 - 149]

NCERT solutions for Mathematics [English] Class 8 12 Factorisation EXERCISE 12.1 [Pages 148 - 149]

EXERCISE 12.1 | Q 1. (i) | Page 148

Find the common factors of the terms.

12x, 36

EXERCISE 12.1 | Q 1. (ii) | Page 148

Find the common factors of the terms.

2y, 22xy

EXERCISE 12.1 | Q 1. (iii) | Page 148

Find the common factors of the terms.

14pq, 28p²q²

EXERCISE 12.1 | Q 1. (iv) | Page 148

Find the common factors of the terms.

2x, 3x², 4

EXERCISE 12.1 | Q 1. (v) | Page 148

Find the common factors of the terms.

6 abc, 24ab², 12a²b

EXERCISE 12.1 | Q 1. (vi) | Page 148

Find the common factors of the terms.

16x³, −4x², 32x

EXERCISE 12.1 | Q 1. (vii) | Page 148

Find the common factors of the terms.

10pq, 20qr, 30rp

EXERCISE 12.1 | Q 1. (viii) | Page 148

Find the common factors of the terms.

3x²y³, 10x³y², 6x²y²z

EXERCISE 12.1 | Q 2. (i) | Page 148

Factorise the following expression:

7x − 42

EXERCISE 12.1 | Q 2. (ii) | Page 148

Factorise the following expression:

6p − 12q

EXERCISE 12.1 | Q 2. (iii) | Page 148

Factorise the following expression:

7a² + 14a

EXERCISE 12.1 | Q 2. (iv) | Page 148

Factorise the following expression:

−16z + 20z³

EXERCISE 12.1 | Q 2. (v) | Page 148

Factorise the following expression:

20 l²m + 30 alm

EXERCISE 12.1 | Q 2. (vi) | Page 148

Factorise the following expression:

5x²y − 15xy²

EXERCISE 12.1 | Q 2. (vii) | Page 148

Factorise the following expression:

10a² − 15b² + 20c²

EXERCISE 12.1 | Q 2. (viii) | Page 148

Factorise the following expression:

− 4a² + 4ab − 4 ca

EXERCISE 12.1 | Q 2. (ix) | Page 148

Factorise the following expression:

x²yz + xy²z + xyz²

EXERCISE 12.1 | Q 2. (x) | Page 148

Factorise the following expression:

ax²y + bxy² + cxyz

EXERCISE 12.1 | Q 3. (i) | Page 148

Factorise.

x² + xy + 8x + 8y

EXERCISE 12.1 | Q 3. (ii) | Page 148

Factorise.

15xy − 6x + 5y − 2

EXERCISE 12.1 | Q 3. (iii) | Page 149

Factorise.

ax + bx − ay − by

EXERCISE 12.1 | Q 3. (iv) | Page 149

Factorise.

15pq + 15 + 9q + 25p

EXERCISE 12.1 | Q 3. (v) | Page 149

Factorise.

z − 7 + 7xy − xyz

EXERCISE 12.2 [Pages 151 - 152]

NCERT solutions for Mathematics [English] Class 8 12 Factorisation EXERCISE 12.2 [Pages 151 - 152]

EXERCISE 12.2 | Q 1. (i) | Page 151

Factorise the following expression.

a² + 8a + 16

EXERCISE 12.2 | Q 1. (ii) | Page 151

Factorise the following expression.

p² − 10p + 25

EXERCISE 12.2 | Q 1. (iii) | Page 151

Factorise the following expression.

25m² + 30m + 9

EXERCISE 12.2 | Q 1. (iv) | Page 151

Factorise the following expression.

49y² + 84yz + 36z²

EXERCISE 12.2 | Q 1. (v) | Page 151

Factorise the following expression.

4x² − 8x + 4

EXERCISE 12.2 | Q 1. (vi) | Page 151

Factorise the following expression.

121b² − 88bc + 16c²

EXERCISE 12.2 | Q 1. (vii) | Page 151

Factorise the following expression.

(l + m)² − 4lm (Hint: Expand (l + m)² first)

EXERCISE 12.2 | Q 1. (viii) | Page 151

Factorise the following expression.

a⁴ + 2a²b² + b⁴

EXERCISE 12.2 | Q 2. (i) | Page 151

Factorise.

4p²− 9q²

EXERCISE 12.2 | Q 2. (ii) | Page 151

Factorise.

63a² − 112b²

EXERCISE 12.2 | Q 2. (iii) | Page 151

Factorise.

49x² − 36

EXERCISE 12.2 | Q 2. (iv) | Page 151

Factorise.

16x⁵ − 144x³

EXERCISE 12.2 | Q 2. (v) | Page 151

Factorise.

(l + m)² − (l − m)²

EXERCISE 12.2 | Q 2. (vi) | Page 151

Factorise.

9x²y² − 16

EXERCISE 12.2 | Q 2. (vii) | Page 151

Factorise.

(x² − 2xy + y²) − z²

EXERCISE 12.2 | Q 2. (viii) | Page 151

Factorise.

25a² − 4b²+ 28bc − 49c²

EXERCISE 12.2 | Q 3. (i) | Page 151

Factorise the expression.

ax² + bx

EXERCISE 12.2 | Q 3. (ii) | Page 151

Factorise the expression.

7p² + 21q²

EXERCISE 12.2 | Q 3. (iii) | Page 151

Factorise the expression.

2x³ + 2xy² + 2xz²

EXERCISE 12.2 | Q 3. (iv) | Page 151

Factorise the expression.

am² + bm² + bn² + an²

EXERCISE 12.2 | Q 3. (v) | Page 151

Factorise the expression.

(lm + l) + m + 1

EXERCISE 12.2 | Q 3. (vi) | Page 151

Factorise the expression.

y (y + z) + 9 (y + z)

EXERCISE 12.2 | Q 3. (vii) | Page 151

Factorise the expression.

5y² − 20y − 8z + 2yz

EXERCISE 12.2 | Q 3. (viii) | Page 151

Factorise the expression.

10ab + 4a + 5b + 2

EXERCISE 12.2 | Q 3. (ix) | Page 151

Factorise the expression.

6xy − 4y + 6 − 9x

EXERCISE 12.2 | Q 4. (i) | Page 152

Factorise.

a⁴ − b⁴

EXERCISE 12.2 | Q 4. (ii) | Page 152

Factorise.

p⁴ − 81

EXERCISE 12.2 | Q 4. (iii) | Page 152

Factorise.

x⁴ − (y + z)⁴

EXERCISE 12.2 | Q 4. (iv) | Page 152

Factorise.

x⁴ − (x − z)⁴

EXERCISE 12.2 | Q 4. (v) | Page 152

Factorise.

a⁴ − 2a²b² + b⁴

EXERCISE 12.2 | Q 5. (i) | Page 152

Factorise the following expression.

p² + 6p + 8

EXERCISE 12.2 | Q 5. (ii) | Page 152

Factorise the given expression.

q² − 10q + 21

EXERCISE 12.2 | Q 5. (iii) | Page 152

Factorise the given expression.

p² + 6p − 16

EXERCISE 12.3 [Page 155]

NCERT solutions for Mathematics [English] Class 8 12 Factorisation EXERCISE 12.3 [Page 155]

EXERCISE 12.3 | Q 1. (i) | Page 155

Carry out the following division:

28x⁴ ÷ 56x

EXERCISE 12.3 | Q 1. (ii) | Page 155

Carry out the following divisions:

−36y³ ÷ 9y²

EXERCISE 12.3 | Q 1. (iii) | Page 155

Carry out the following divisions:

66pq²r³ ÷ 11qr²

EXERCISE 12.3 | Q 1. (iv) | Page 155

Carry out the following divisions:

34x³y³z³ ÷ 51xy²z³

EXERCISE 12.3 | Q 1. (v) | Page 155

Carry out the following divisions:

12a⁸b⁸ ÷ (−6a⁶b⁴)

EXERCISE 12.3 | Q 2. (i) | Page 155

Divide the given polynomial by the given monomial.

(5x² − 6x) ÷ 3x

EXERCISE 12.3 | Q 2. (ii) | Page 155

Divide the given polynomial by the given monomial.

(3y⁸− 4y⁶ + 5y⁴) ÷ y⁴

EXERCISE 12.3 | Q 2. (iii) | Page 155

Divide the given polynomial by the given monomial.

8(x³y²z² + x²y³z² + x²y²z³) ÷ 4x²y²z²

EXERCISE 12.3 | Q 2. (iv) | Page 155

Divide the given polynomial by the given monomial.

(x³ + 2x² + 3x) ÷ 2x

EXERCISE 12.3 | Q 2. (v) | Page 155

Divide the given polynomial by the given monomial.

(p³q⁶ − p⁶q³) ÷ p³q³

EXERCISE 12.3 | Q 3. (i) | Page 155

Work out the following division:

(10x − 25) ÷ 5

EXERCISE 12.3 | Q 3. (ii) | Page 155

Work out the following division:

(10x − 25) ÷ (2x − 5)

EXERCISE 12.3 | Q 3. (iii) | Page 155

Work out the following division:

10y(6y + 21) ÷ 5(2y + 7)

EXERCISE 12.3 | Q 3. (iv) | Page 155

Work out the following division:

9x²y²(3z − 24) ÷ 27xy(z − 8)

EXERCISE 12.3 | Q 3. (v) | Page 155

Work out the following division:

96abc(3a − 12)(5b − 30) ÷ 144(a − 4) (b − 6)

EXERCISE 12.3 | Q 4. (i) | Page 155

Divide as directed.

5(2x + 1) (3x + 5) ÷ (2x + 1)

EXERCISE 12.3 | Q 4. (ii) | Page 155

Divide as directed.

26xy(x + 5) (y − 4) ÷ 13x(y − 4)

EXERCISE 12.3 | Q 4. (iii) | Page 155

Divide as directed.

52pqr (p + q) (q + r) (r + p) ÷ 104pq (q + r) (r + p)

EXERCISE 12.3 | Q 4. (iv) | Page 155

Divide as directed.

20(y + 4) (y² + 5y + 3) ÷ 5(y + 4)

EXERCISE 12.3 | Q 4. (v) | Page 155

Divide as directed.

x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)

EXERCISE 12.3 | Q 5. (i) | Page 155

Factorise the expression and divide them as directed.

(y² + 7y + 10) ÷ (y + 5)

EXERCISE 12.3 | Q 5. (ii) | Page 155

Factorise the expression and divide them as directed.

(m² − 14m − 32) ÷ (m + 2)

EXERCISE 12.3 | Q 5. (iii) | Page 155

Factorise the expression and divide them as directed.

(5p² − 25p + 20) ÷ (p − 1)

EXERCISE 12.3 | Q 5. (iv) | Page 155

Factorise the expression and divide them as directed.

4yz(z² + 6z − 16) ÷ 2y(z + 8)

EXERCISE 12.3 | Q 5. (v) | Page 155

Factorise the expression and divide them as directed.

5pq(p² − q²) ÷ 2p(p + q)

EXERCISE 12.3 | Q 5. (vi) | Page 155

Factorise the expression and divide them as directed.

12xy(9x² − 16y²) ÷ 4xy(3x + 4y)

EXERCISE 12.3 | Q 5. (vii) | Page 155

Factorise the expression and divide them as directed.

39y³(50y²− 98) ÷ 26y²(5y + 7)

Solutions for 12: Factorisation

EXERCISE 12.1EXERCISE 12.2EXERCISE 12.3

NCERT solutions for Mathematics [English] Class 8 chapter 12 - Factorisation - Shaalaa.com

NCERT solutions for Mathematics [English] Class 8 chapter 12 - Factorisation

Shaalaa.com has the CBSE Mathematics Mathematics [English] Class 8 CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Mathematics [English] Class 8 CBSE 12 (Factorisation) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Mathematics [English] Class 8 chapter 12 Factorisation are Factors and Multiples, Factorisation by Taking Out Common Factors, Factorising Algebraic Expressions, Factorisation by Regrouping Terms, Factorisation Using Identities, Factors of the Form (x + a)(x + b), Dividing a Monomial by a Monomial, Dividing a Polynomial by a Monomial, Dividing a Polynomial by a Polynomial, Concept of Find the Error, Factors and Multiples, Factorisation by Taking Out Common Factors, Factorising Algebraic Expressions, Factorisation by Regrouping Terms, Factorisation Using Identities, Factors of the Form (x + a)(x + b), Dividing a Monomial by a Monomial, Dividing a Polynomial by a Monomial, Dividing a Polynomial by a Polynomial, Concept of Find the Error.

Using NCERT Mathematics [English] Class 8 solutions Factorisation exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics [English] Class 8 students prefer NCERT Textbook Solutions to score more in exams.

Get the free view of Chapter 12, Factorisation Mathematics [English] Class 8 additional questions for Mathematics Mathematics [English] Class 8 CBSE, and you can use Shaalaa.com to keep it handy for your exam preparation.

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