In this page we have class 8 maths exercise 14.3 solutions
class 8 maths exercise 14.3 solutions
Question 1
Carry out the following divisions.
(i) 28x
4 ÷ 56x
(ii) –36y³ ÷ 9y²
(iii) 66pq²r
3 ÷ 11qr²
(iv) 34x
3 y
3 z
3 ÷ 51xy²z
3
(v) 12a
8 b
8 ÷ (– 6a
6 b
4 )
Answer :
(i) 28x
4 ÷ 56x
= (2×2×7×x×x
3 ) /( 2×2×2×7×x)
=x
3 /2
(ii) –36y³ ÷ 9y²
= (-2×2×3×3×y×y
2 ) /( 3×3×y
2 )
=-4y
(iii) 66pq²r
3 ÷ 11qr²
= 6pqr
(iv) 34x
3 y
3 z
3 ÷ 51xy²z
3
=(2/3) x
2 y
(v) 12a
8 b
8 ÷ (– 6a
6 b
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
3 y²z² + x²y
3 z² + x²y²z
3 ) ÷ 4x²y²z²
(iv) (x
3 + 2x² + 3x) ÷ 2x
(v) (p
3 q
6 – p
6 q
3 ) ÷ p
3 q
3
Answer:
(i)(5x² – 6x) ÷ 3x
=[x(5x-6)] / 3x
Cancelling x
=(5x-6)/3
(ii)(3y
8 – 4y
6 + 5y
4 ) ÷ y
4
= y
4 (3y
4 -4y
2 +5)/ y
4
=3y
4 -4y²+5
(iii)8(x
3 y²z² + x²y
3 z² + x²y²z
3 ) ÷ 4x²y²z²
=8x
2 y²z²(x+y+z)/ 4x²y²z²
= 2(x+y+z)
(iv)(x
3 + 2x² + 3x) ÷ 2x
=x(x
2 +2x+3)/2x
=( x
2 +2x+3)/2
(v)(p
3 q
6 – p
6 q
3 ) ÷ p
3 q
3
= p
3 q
3 (q
3 - p
3 ) / p
3 q
3
=(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
(i) (10x – 25) ÷ 5
=5(2x-5)/5
=(2x-5)
(ii) (10x – 25) ÷ (2x – 5)
= 5(2x-5) /(2x – 5)
=-5
(iii) 10y(6y + 21) ÷ 5(2y + 7)
=30y(2y+7)/ 5(2y + 7)
= 6y
(iv) 9x²y² (3z – 24) ÷ 27xy(z – 8)
=27 x²y²(z-8)/ 27xy(z – 8)
=xy
(v) 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) (
y 2 + 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) (
y 2 + 5
y + 3) ÷ 5(
y + 4)
=4(
y 2 + 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) (
y 2 + 7
y + 10) ÷ (
y + 5)
(ii) (
m 2 - 14
m - 32) ÷ (
m + 2)
(iii) (5
p 2 - 25
p + 20) ÷ (
p - 1)
(iv) 4
yz (
z 2 + 6
z - 16) ÷ 2
y (
z + 8)
(v) 5
pq (
p 2 -
q 2 ) ÷ 2
p (
p +
q )
(vi) 12
xy (9
x 2 - 16
y 2 ) ÷ 4
xy (3
x + 4
y )
(vii) 39
y 3 (50
y 2 - 98) ÷ 26
y 2 (5
y + 7)
Answer
(i)(
y 2 + 7
y + 10) ÷ (
y + 5)
=(
y 2 + 5
y+2y + 10)/(y+5)
=[y(y+5)+2(y+5)] /(y+5)
=(y+1)(y+5) /(y+5)
=(y+1)
(ii) (
m 2 - 14
m - 32) ÷ (
m + 2)
= (
m 2 - 16
m+2m - 32) / (
m + 2)
=[m(m-16)+2(m-16)] /(m+2)
=(m+2)(m-16) /(m+2
=(m-16)
(iii) (5
p 2 - 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 (
z 2 + 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 (
p 2 -
q 2 ) ÷ 2
p (
p +
q )
=5
pq (
p 2 -
q 2 ) / 2
p (
p +
q )
=5pq(p-q)(p+q) / 2
p (
p +
q )
=5q(p-q)/2
(vi) 12
xy (9
x 2 - 16
y 2 ) ÷ 4
xy (3
x + 4
y )
=12
xy (9
x 2 - 16
y 2 ) / 4
xy (3
x + 4
y )
=12xy(3x+4y)(3x-4y) / 4
xy (3
x + 4
y )
=3(3x-4y)
(vii) 39
y 3 (50
y 2 - 98) ÷ 26
y 2 (5
y + 7)
=39
y 3 (50
y 2 - 98) /26
y 2 (5
y + 7)
=78y
3 (25y
2 -49)/ 26
y 2 (5
y + 7)
=3y(5y+7)(5y-7)/ (5
y + 7)
=3y(5y-7)
Summary
class 8 maths exercise 14.3 solutions has been prepared by Expert with utmost care. If you find any mistake.Please do provide feedback on mail. You can download the solutions as PDF in the below Link also Download Factorisation Exercise 14.3 pdf
This chapter 14 has total 4 Exercise 14.1,14.2,14.3 and 14.4. This is the Third exercise in the chapter.You can explore previous exercise of this chapter by clicking the link below
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