In this page we have NCERT book Solutions for Class 8th Maths Chapter 14:Factorization for
Exercise 14.3. Hope you like them and do not forget to like , social share
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Question 1
Carry out the following divisions.
(i) 28x
4 ÷ 56x
(ii) –36y³ ÷ 9y²
(iii) 66pq²r
3 ÷ 11qr²
(iv) 34x
3y
3z
3 ÷ 51xy²z
3
(v) 12a
8b
8 ÷ (– 6a
6b
4)
Answer:
1) 28x
4 ÷ 56x
= (2×2×7×x×x
3 ) /( 2×2×2×7×x)
=x
3/2
2) –36y³ ÷ 9y²
= (-2×2×3×3×y×y
2 ) /( 3×3×y
2)
=-4y
3) 66pq²r
3 ÷ 11qr²
= 6pqr
4) 34x
3y
3z
3 ÷ 51xy²z
3
=(2/3) x
2y
5) 12a
8b
8 ÷ (– 6a
6b
4)
=-2a²b
4
Question 2
Divide the given polynomial by the given monomial.
(i) (5x² – 6x) ÷ 3x
(ii) (3y
8 – 4y
6 + 5y
4) ÷ y
4
(iii) 8(x
3y²z² + x²y
3z² + x²y²z
3) ÷ 4x²y²z²
(iv) (x
3 + 2x² + 3x) ÷ 2x
(v) (p
3q
6 – p
6q
3) ÷ p
3q
3
Answer:
- (5x² – 6x) ÷ 3x
=[x(5x-6)] / 3x
Cancelling x
=(5x-6)/3
- (3y8 – 4y6 + 5y4) ÷ y4
= y4(3y4 -4y2 +5)/ y4
=3y4-4y²+5
- 8(x3y²z² + x²y3z² + x²y²z3) ÷ 4x²y²z²
=8x2 y²z²(x+y+z)/ 4x²y²z²
= 2(x+y+z)
- (x3 + 2x² + 3x) ÷ 2x
=x(x2 +2x+3)/2x
=( x2 +2x+3)/2
- (p3q6 – p6q3) ÷ p3q3
= p3 q3(q3 - p3) / p3q3
=(q
3 - p
3)
Question 3
Work out the following divisions.
(i) (10x – 25) ÷ 5
(ii) (10x – 25) ÷ (2x – 5)
(iii) 10y(6y + 21) ÷ 5(2y + 7)
(iv) 9x²y² (3z – 24) ÷ 27xy(z – 8)
(v) 96abc(3a – 12) (5b – 30) ÷ 144(a – 4) (b – 6)
Answer
1) (10x – 25) ÷ 5
=5(2x-5)/5
=(2x-5)
2) (10x – 25) ÷ (2x – 5)
= 5(2x-5) /(2x – 5)
=-5
3) 10y(6y + 21) ÷ 5(2y + 7)
=30y(2y+7)/ 5(2y + 7)
= 6y
4) 9x²y² (3z – 24) ÷ 27xy(z – 8)
=27 x²y²(z-8)/ 27xy(z – 8)
=xy
5) 96abc(3a – 12) (5b – 30) ÷ 144(a – 4) (b – 6)
=(96×3×5)abc(a-4)(b-6)/ 144(a – 4) (b – 6)
=10abc
Question 4
Divide as directed.
(i) 5(2
x + 1) (3
x + 5) ÷ (2
x + 1)
(ii) 26
xy(
x + 5) (
y - 4) ÷ 13
x(
y - 4)
(iii) 52
pqr (
p +
q) (
q +
r) (
r +
p) ÷ 104
pq(
q +
r) (
r +
p)
(iv) 20(
y + 4) (
y2 + 5
y + 3) ÷ 5(
y + 4)
(v)
x(
x + 1) (
x + 2) (
x + 3) ÷
x(
x + 1)
Answer
i) 5(2
x + 1) (3
x + 5) ÷ (2
x + 1)
=5(2
x + 1) (3
x + 5) / (2
x + 1)
=5(3x+5)
ii) 26
xy(
x + 5) (
y - 4) ÷ 13
x(
y - 4)
=26
xy(
x + 5) (
y - 4) / 13
x(
y - 4)
Cancelling 13x(y-4)
=2y(x+5)
iii) 52
pqr (
p +
q) (
q +
r) (
r +
p) ÷ 104
pq(
q +
r) (
r +
p)
=52
pqr (
p +
q) (
q +
r) (
r +
p)/ 104
pq(
q +
r) (
r +
p)
Cancelling 52pq(
q +
r) (
r +
p)
=r(p+q)/2
iv) 20(
y + 4) (
y2 + 5
y + 3) ÷ 5(
y + 4)
=4(
y2 + 5
y + 3)
v) x(
x + 1) (
x + 2) (
x + 3) ÷
x(
x + 1)
=
x(
x + 1) (
x + 2) (
x + 3) /
x(
x + 1)
Cancelling
x(
x + 1)
=(
x + 2) (
x + 3)
Question 5
Factorize the expressions and divide them as directed.
(i) (
y2 + 7
y + 10) ÷ (
y + 5)
(ii) (
m2 - 14
m - 32) ÷ (
m + 2)
(iii) (5
p2 - 25
p + 20) ÷ (
p - 1)
(iv) 4
yz(
z2 + 6
z - 16) ÷ 2
y(
z + 8)
(v) 5
pq(
p2 -
q2) ÷ 2
p(
p +
q)
(vi) 12
xy(9
x2 - 16
y2) ÷ 4
xy(3
x + 4
y)
(vii) 39
y3(50
y2- 98) ÷ 26
y2(5
y+ 7)
Answer
i) (
y2 + 7
y + 10) ÷ (
y + 5)
=(
y2 + 5
y+2y + 10)/(y+5)
=[y(y+5)+2(y+5)] /(y+5)
=(y+1)(y+5) /(y+5)
=(y+1)
ii) (
m2 - 14
m - 32) ÷ (
m + 2)
= (
m2 - 16
m+2m - 32) / (
m + 2)
=[m(m-16)+2(m-16)] /(m+2)
=(m+2)(m-16) /(m+2
=(m-16)
iii) (5
p2 - 25
p + 20) ÷ (
p - 1)
=5(p
2-5p+4)/(p-1)
=5[p(p-1) -4(p-1)] /(p-1)
=5(p-1)(p-4)/(p-1)
=5(p-4)
iv) 4
yz(
z2 + 6
z - 16) ÷ 2
y(
z + 8)
=4yz[z
2 -2z+8z-16]/ 2
y(
z + 8)
=4yz[z(z-2)+8(z-2)] / 2
y(
z + 8)
=4yz(z-2)(z+8) / 2
y(
z + 8)
=2z(z-2)
v) 5
pq(
p2 -
q2) ÷ 2
p(
p +
q)
=5
pq(
p2 -
q2) / 2
p(
p +
q)
=5pq(p-q)(p+q) / 2
p(
p +
q)
=5q(p-q)/2
vi) 12
xy(9
x2 - 16
y2) ÷ 4
xy(3
x + 4
y)
=12
xy(9
x2 - 16
y2) / 4
xy(3
x + 4
y)
=12xy(3x+4y)(3x-4y) / 4
xy(3
x + 4
y)
=3(3x-4y)
vii) 39
y3(50
y2- 98) ÷ 26
y2(5
y+ 7)
=39
y3(50
y2- 98) /26
y2(5
y+ 7)
=78y
3(25y
2-49)/ 26
y2(5
y+ 7)
=3y(5y+7)(5y-7)/ (5
y+ 7)
=3y(5y-7)
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