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NCERT solutions Mathematics Class 8 chapter 14 Factorisation

Chapters

NCERT Mathematics Class 8

Mathematics Textbook for Class 8

Chapter 14 - Factorisation

Page 220

Find the common factors of the terms

12x, 36

Q 1.1 | Page 220

Find the common factors of the terms

2y, 22xy

Q 1.2 | Page 220

Find the common factors of the terms

14pq, 28p2q2

Q 1.3 | Page 220

Find the common factors of the terms

2x, 3x2, 4

Q 1.4 | Page 220

Find the common factors of the terms

6abc, 24ab2, 12a2b

Q 1.5 | Page 220

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

 

Q 1.6 | Page 220

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

Q 1.7 | Page 220

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

 

Q 1.8 | Page 220

Factorise the given expressions ax2y + bxy2 + cxyz

Q 2.1 | Page 220

Factorise the given expressions 7x − 42

Q 2.1 | Page 220

Factorise the given expressions  6p − 12q

Q 2.2 | Page 220

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

Q 2.3 | Page 220

Factorise the given expressions  7a2 + 14a

Q 2.3 | Page 220

Factorise the given expressions −16z + 20z3

 

Q 2.4 | Page 220

Factorise the given expressions 20l2m + 30 alm

Q 2.5 | Page 220

Factorise the given expressions  5x2y − 15xy2

Q 2.6 | Page 220

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

Q 2.7 | Page 220

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

Q 2.8 | Page 220

Factorise the given expressions x2yz + xy2z + xyz2

Q 2.9 | Page 220

Factorise x2 + xy + 8x + 8y

Q 3.1 | Page 220

Factorise 15xy − 6x + 5y − 2

Q 3.2 | Page 220

Factorise ax + bx − ay − by

Q 3.3 | Page 220

Factorise 15pq + 15 + 9q + 25p

Q 3.4 | Page 220

Factorise z − 7 + 7xy − xyz

Q 3.5 | Page 220

Pages 223 - 224

Factorise the given expressions.

a2 + 8a + 16

Q 1.1 | Page 223

Factorise the given expressions.

p2 − 10p + 25

Q 1.2 | Page 223

Factorise the given expressions.

25m2 + 30m + 9

Q 1.3 | Page 223

Factorise the given expressions.

49y2 + 84yz + 36z2

Q 1.4 | Page 223

Factorise the given expressions.

4x2 − 8x + 4

Q 1.5 | Page 223

Factorise the given expressions.

121b2 − 88bc + 16c2

Q 1.6 | Page 223

Factorise the given expressions.

a4 + 2a2b2 + b4

Q 1.8 | Page 223

Factorise  4p− 9q2

Q 2.1 | Page 223

Factorise 63a2 − 112b2

Q 2.2 | Page 223

Factorise 49x2 − 36

Q 2.3 | Page 223

Factorise 16x5 − 144x3

Q 2.4 | Page 223

Factorise (l + m)2 − (l − m)2

Q 2.5 | Page 223

Factorise  9x2y2 − 16

Q 2.6 | 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 2.7 | Page 223

Factorise 25a2 − 4b+ 28bc − 49c2

Q 2.8 | Page 223

Factorise the expressions ax2 + bx

Q 3.1 | Page 223

Factorise the expressions 7p2 + 21q2

Q 3.2 | Page 223

Factorise the expressions 2x3 + 2xy2 + 2xz2

Q 3.3 | Page 223

Factorise the expressions am2 + bm2 + bn2 + an2

Q 3.4 | Page 223

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

Q 3.5 | Page 223

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

Q 3.6 | Page 223

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

Q 3.7 | Page 223

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

Q 3.8 | Page 223

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

Q 3.9 | Page 223

Factorise a4 − b4

Q 4.1 | Page 224

Factorise p4 − 81

Q 4.2 | Page 224

Factorise x4 − (y + z)4

Q 4.3 | Page 224

Factorise x4 − (x − z)4

Q 4.4 | Page 224

Factorise a4 − 2a2b2 + b4

Q 4.5 | Page 224

Factorise the given expressions p2 + 6p + 8

 

Q 5.1 | Page 224

Factorise the given expressions. q2 − 10q + 21

Q 5.2 | Page 224

Factorise the given expressions.

p2 + 6p − 16

Q 5.3 | Page 224

Page 227

Carry out the following divisions.

28x4 ÷ 56x

Q 1.1 | Page 227

Carry out the following divisions

−36y3 ÷ 9y2

Q 1.2 | Page 227

Carry out the following divisions.

66pq2r3 ÷ 11qr2

Q 1.3 | Page 227

Carry out the following divisions.

34x3y3z3 ÷ 51xy2z3

Q 1.4 | Page 227

Carry out the following divisions.

12a8b8 ÷ (−6a6b4)

Q 1.5 | Page 227

Divide the given polynomial by the given monomial.

(5x2 − 6x) ÷ 3x

Q 2.1 | Page 227

Divide the given polynomial by the given monomial.

(3y− 4y6 + 5y4) ÷ y4

Q 2.2 | Page 227

Divide the given polynomial by the given monomial.

8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2

Q 2.3 | Page 227

Divide the given polynomial by the given monomial.

(x3 + 2x2 + 3x) ÷ 2x

Q 2.4 | Page 227

Divide the given polynomial by the given monomial.

(p3q6 − p6q3) ÷ p3q3

Q 2.5 | Page 227

Work out the following divisions.

(10x − 25) ÷ 5

Q 3.1 | Page 227

Work out the following divisions.

(10x − 25) ÷ (2x − 5)

Q 3.2 | Page 227

Work out the following divisions.

10y(6y + 21) ÷ 5(2y + 7)

Q 3.3 | Page 227

Work out the following divisions.

9x2y2(3z − 24) ÷ 27xy(z − 8)

Q 3.4 | Page 227

Work out the following divisions.

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

Q 3.5 | Page 227

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

Q 4.1 | Page 227

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

Q 4.2 | Page 227

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

Q 4.3 | Page 227

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

Q 4.4 | Page 227

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

Q 4.5 | Page 227

Factorise the expressions and divide them as directed.

(y2 + 7y + 10) ÷ (y + 5)

Q 5.1 | Page 227

Factorise the expressions and divide them as directed.

(m2 − 14m − 32) ÷ (m + 2)

Q 5.2 | Page 227

Factorise the expressions and divide them as directed.

 (5p2 − 25p + 20) ÷ (p − 1)

Q 5.3 | Page 227

Factorise the expressions and divide them as directed.

4yz(z2 + 6z − 16) ÷ 2y(z + 8)

Q 5.4 | Page 227

Factorise the expressions and divide them as directed.

5pq(p2 − q2) ÷ 2p(p + q)

Q 5.5 | Page 227

Factorise the expressions and divide them as directed.

12xy(9x2 − 16y2) ÷ 4xy(3x + 4y)

Q 5.6 | Page 227

Factorise the expressions and divide them as directed.

39y3(50y2− 98) ÷ 26y2(5y+ 7)

Q 5.7 | Page 227

Pages 228 - 229

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

Q 1 | Page 228

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

Q 2 | Page 228

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

Q 3 | Page 228

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

Q 4 | Page 228

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

Q 6 | Page 228

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

Q 7 | Page 228

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

Q 8 | Page 228

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

Q 9 | Page 228

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 10.1 | 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 − 15 + 4 = −2

Q 10.2 | 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 10.3 | Page 229

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

Q 11 | Page 229

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

Q 12 | Page 229

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

Q 13 | Page 229

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

Q 14 | Page 229

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

Q 15 | Page 229

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

Q 16 | Page 229

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

Q 17 | Page 229

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

Q 18 | Page 229

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

Q 19 | Page 229

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

Q 20 | Page 229

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

Q 21 | Page 229

Page 228

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

Q 5 | Page 228

NCERT Mathematics Class 8

Mathematics Textbook for Class 8
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