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# NCERT solutions for Class 8 Mathematics chapter 14 - Factorisation

## Chapter 14 - Factorisation

#### Page 220

Q 1.1 | Page 220

Find the common factors of the terms

12x, 36

Q 1.2 | Page 220

Find the common factors of the terms

2y, 22xy

Q 1.3 | Page 220

Find the common factors of the terms

14pq, 28p2q2

Q 1.4 | Page 220

Find the common factors of the terms

2x, 3x2, 4

Q 1.5 | Page 220

Find the common factors of the terms

6abc, 24ab2, 12a2b

Q 1.6 | Page 220

Find the common factors of the terms 16x3, −4x2, 32x

Q 1.7 | Page 220

Find the common factors of the terms 10pq, 20qr, 30rp

Q 1.8 | Page 220

Find the common factors of the terms 3x2y3, 10x3y2, 6x2y2z

Q 2.1 | Page 220

Factorise the given expressions ax2y + bxy2 + cxyz

Q 2.1 | Page 220

Factorise the given expressions 7x − 42

Q 2.2 | Page 220

Factorise the given expressions  6p − 12q

Q 2.3 | Page 220

Find the common factors of the terms 7a2 + 14a

Q 2.3 | Page 220

Factorise the given expressions  7a2 + 14a

Q 2.4 | Page 220

Factorise the given expressions −16z + 20z3

Q 2.5 | Page 220

Factorise the given expressions 20l2m + 30 alm

Q 2.6 | Page 220

Factorise the given expressions  5x2y − 15xy2

Q 2.7 | Page 220

Factorise the given expressions 10a2 − 15b2 + 20c2

Q 2.8 | Page 220

Factorise the given expressions  −4a2 + 4ab − 4 ca

Q 2.9 | Page 220

Factorise the given expressions x2yz + xy2z + xyz2

Q 3.1 | Page 220

Factorise x2 + xy + 8x + 8y

Q 3.2 | Page 220

Factorise 15xy − 6x + 5y − 2

Q 3.3 | Page 220

Factorise ax + bx − ay − by

Q 3.4 | Page 220

Factorise 15pq + 15 + 9q + 25p

Q 3.5 | Page 220

Factorise z − 7 + 7xy − xyz

#### Pages 223 - 224

Q 1.1 | Page 223

Factorise the given expressions.

a2 + 8a + 16

Q 1.2 | Page 223

Factorise the given expressions.

p2 − 10p + 25

Q 1.3 | Page 223

Factorise the given expressions.

25m2 + 30m + 9

Q 1.4 | Page 223

Factorise the given expressions.

49y2 + 84yz + 36z2

Q 1.5 | Page 223

Factorise the given expressions.

4x2 − 8x + 4

Q 1.6 | Page 223

Factorise the given expressions.

121b2 − 88bc + 16c2

Q 1.8 | Page 223

Factorise the given expressions.

a4 + 2a2b2 + b4

Q 2.1 | Page 223

Factorise  4p− 9q2

Q 2.2 | Page 223

Factorise 63a2 − 112b2

Q 2.3 | Page 223

Factorise 49x2 − 36

Q 2.4 | Page 223

Factorise 16x5 − 144x3

Q 2.5 | Page 223

Factorise (l + m)2 − (l − m)2

Q 2.6 | Page 223

Factorise  9x2y2 − 16

Q 2.7 | Page 223

Factorise the given expressions.

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

Q 2.7 | Page 223

Factorise (x2 − 2xy + y2) − z2

Q 2.8 | Page 223

Factorise 25a2 − 4b+ 28bc − 49c2

Q 3.1 | Page 223

Factorise the expressions ax2 + bx

Q 3.2 | Page 223

Factorise the expressions 7p2 + 21q2

Q 3.3 | Page 223

Factorise the expressions 2x3 + 2xy2 + 2xz2

Q 3.4 | Page 223

Factorise the expressions am2 + bm2 + bn2 + an2

Q 3.5 | Page 223

Factorise the expressions (lm + l) + m + 1

Q 3.6 | Page 223

Factorise the expressions  y(y + z) + 9(y + z)

Q 3.7 | Page 223

Factorise the expressions 5y2 − 20y − 8z + 2yz

Q 3.8 | Page 223

Factorise the expressions 10ab + 4a + 5b + 2

Q 3.9 | Page 223

Factorise the expressions 6xy − 4y + 6 − 9x

Q 4.1 | Page 224

Factorise a4 − b4

Q 4.2 | Page 224

Factorise p4 − 81

Q 4.3 | Page 224

Factorise x4 − (y + z)4

Q 4.4 | Page 224

Factorise x4 − (x − z)4

Q 4.5 | Page 224

Factorise a4 − 2a2b2 + b4

Q 5.1 | Page 224

Factorise the given expressions p2 + 6p + 8

Q 5.2 | Page 224

Factorise the given expressions. q2 − 10q + 21

Q 5.3 | Page 224

Factorise the given expressions.

p2 + 6p − 16

#### Page 227

Q 1.1 | Page 227

Carry out the following divisions.

28x4 ÷ 56x

Q 1.2 | Page 227

Carry out the following divisions

−36y3 ÷ 9y2

Q 1.3 | Page 227

Carry out the following divisions.

66pq2r3 ÷ 11qr2

Q 1.4 | Page 227

Carry out the following divisions.

34x3y3z3 ÷ 51xy2z3

Q 1.5 | Page 227

Carry out the following divisions.

12a8b8 ÷ (−6a6b4)

Q 2.1 | Page 227

Divide the given polynomial by the given monomial.

(5x2 − 6x) ÷ 3x

Q 2.2 | Page 227

Divide the given polynomial by the given monomial.

(3y− 4y6 + 5y4) ÷ y4

Q 2.3 | Page 227

Divide the given polynomial by the given monomial.

8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2

Q 2.4 | Page 227

Divide the given polynomial by the given monomial.

(x3 + 2x2 + 3x) ÷ 2x

Q 2.5 | Page 227

Divide the given polynomial by the given monomial.

(p3q6 − p6q3) ÷ p3q3

Q 3.1 | Page 227

Work out the following divisions.

(10x − 25) ÷ 5

Q 3.2 | Page 227

Work out the following divisions.

(10x − 25) ÷ (2x − 5)

Q 3.3 | Page 227

Work out the following divisions.

10y(6y + 21) ÷ 5(2y + 7)

Q 3.4 | Page 227

Work out the following divisions.

9x2y2(3z − 24) ÷ 27xy(z − 8)

Q 3.5 | Page 227

Work out the following divisions.

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

Q 4.1 | Page 227

Divide as directed 5(2x + 1) (3x + 5) ÷ (2x + 1)

Q 4.2 | Page 227

Divide as directed 26xy(x + 5) (y − 4) ÷ 13x(y − 4)

Q 4.3 | Page 227

Divide as directed 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)

Q 4.4 | Page 227

Divide as directed 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4)

Q 4.5 | Page 227

Divide as directed x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)

Q 5.1 | Page 227

Factorise the expressions and divide them as directed.

(y2 + 7y + 10) ÷ (y + 5)

Q 5.2 | Page 227

Factorise the expressions and divide them as directed.

(m2 − 14m − 32) ÷ (m + 2)

Q 5.3 | Page 227

Factorise the expressions and divide them as directed.

(5p2 − 25p + 20) ÷ (p − 1)

Q 5.4 | Page 227

Factorise the expressions and divide them as directed.

4yz(z2 + 6z − 16) ÷ 2y(z + 8)

Q 5.5 | Page 227

Factorise the expressions and divide them as directed.

5pq(p2 − q2) ÷ 2p(p + q)

Q 5.6 | Page 227

Factorise the expressions and divide them as directed.

12xy(9x2 − 16y2) ÷ 4xy(3x + 4y)

Q 5.7 | Page 227

Factorise the expressions and divide them as directed.

39y3(50y2− 98) ÷ 26y2(5y+ 7)

#### Pages 228 - 229

Q 1 | Page 228

Find and correct the errors in the statement: 4(x − 5) = 4x − 5

Q 2 | Page 228

Find and correct the errors in the statement: x(3x + 2) = 3x2 + 2

Q 3 | Page 228

Find and correct the errors in the statement: 2x + 3y = 5xy

Q 4 | Page 228

Find and correct the errors in the statement: x + 2x + 3x = 5x

Q 6 | Page 228

Find and correct the errors in the statement: 3x + 2x = 5x2

Q 7 | Page 228

Find and correct the errors in the statement: (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7

Q 8 | Page 228

Find and correct the errors in the statement: (2x)2 + 5x = 4x + 5x = 9x

Q 9 | Page 228

Find and correct the errors in the statement: (3x + 2)2 = 3x2 + 6x + 4

Q 10.1 | Page 229

Find and correct the errors in the following mathematical statement. Substituting x = −3 in

x2 + 5x + 4 gives (−3)2 + 5 (−3) + 4 = 9 + 2 + 4 = 15

Q 10.2 | Page 229

Find and correct the errors in the following mathematical statement. Substituting x = −3 in

x2 − 5x + 4 gives (−3)2 − 5 (−3) + 4 = 9 − 15 + 4 = −2

Q 10.3 | Page 229

Find and correct the errors in the following mathematical statement. Substituting x = −3 in  x2 + 5x gives (−3)2 + 5 (−3) = −9 − 15 = −24

Q 11 | Page 229

Find and correct the errors in the statement: (y − 3)2 = y2 − 9

Q 12 | Page 229

Find and correct the errors in the statement: (z + 5)2 = z2 + 25

Q 13 | Page 229

Find and correct the errors in the statement: (2a + 3b) (a − b) = 2a2 − 3b2

Q 14 | Page 229

Find and correct the errors in the statement: (a + 4) (a + 2) = a2 + 8

Q 15 | Page 229

Find and correct the errors in the statement: (a − 4) (− 2) = a2 − 8

Q 16 | Page 229

Find and correct the errors in the statement: 3x^2/3x^2 = 0

Q 17 | Page 229

Find and correct the errors in the statement: (3x^2 + 1)/(3x^2) = 1 + 1 = 2

Q 18 | Page 229

Find and correct the errors in the statement: (3x)/(3x + 2) = 1/2

Q 19 | Page 229

Find and correct the errors in the statement : 3/(4x + 3) = 1/(4x)

Q 20 | Page 229

Find and correct the errors in the statement:  (4x + 5)/(4x) = 5

Q 21 | Page 229

Find and correct the errors in the statement: (7x + 5)/5 = 7x

#### Page 228

Q 5 | Page 228

Find and correct the errors in the statement: 5y + 2y + y − 7y = 0

## NCERT solutions for Class 8 Mathematics chapter 14 - Factorisation

NCERT solutions for Class 8 Maths chapter 14 (Factorisation) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Textbook for Class 8 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Mathematics chapter 14 Factorisation are Method of Common Factors, Factorisation by Regrouping Terms, Factorisation Using Identities, Factors of the Form ( x + a) ( x + b), Division of Algebraic Expressions - Division of a Monomial by Another Monomial, Division of Algebraic Expressions - Division of a Polynomial by a Monomial, Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial), Concept of Find the Error, Factors of Natural Numbers, Factors of Algebraic Expressions.

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

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