# class 8 maths exercise 14.3 solutions

In this page we have class 8 maths exercise 14.3 solutions for Factorisation.This exercise has questions on Division of Algebraic Expressions by factorisation method.It includes division of polynomials by monomial, binomial and polynomails . Hope you like them and do not forget to like , social share and comment at the end of the page.

## class 8 maths exercise 14.3 solutions

Question 1
Carry out the following divisions.
(i) 28x4 ÷ 56x
(ii) –36y³ ÷ 9y²
(iii) 66pq²r3 ÷ 11qr²
(iv) 34x3y3z3 ÷ 51xy²z3
(v) 12a8b8 ÷ (– 6a6b4)
Answer:
(i) 28x4 ÷ 56x
= (2×2×7×x×x3  ) /( 2×2×2×7×x)
=x3/2
(ii) –36y³ ÷ 9y²
= (-2×2×3×3×y×y2 ) /( 3×3×y2)
=-4y
(iii) 66pq²r3 ÷ 11qr²
= 6pqr
(iv) 34x3y3z3 ÷ 51xy²z3
=(2/3) x2y
(v) 12a8b8 ÷ (– 6a6b4)
=-2a²b4

Question 2
Divide the given polynomial by the given monomial.
(i) (5x² – 6x) ÷ 3x
(ii) (3y8 – 4y6 + 5y4) ÷ y4
(iii) 8(x3y²z² + x²y3z² + x²y²z3) ÷ 4x²y²z²
(iv) (x3 + 2x² + 3x) ÷ 2x
(v) (p3q6 – p6q3) ÷ p3q3
Answer:
(i)(5x² – 6x) ÷ 3x =[x(5x-6)]  / 3x
Cancelling x
=(5x-6)/3
(ii)(3y8 – 4y6 + 5y4) ÷ y4 = y4(3y4 -4y2 +5)/ y4
=3y4-4y²+5
(iii)8(x3y²z² + x²y3z² + x²y²z3) ÷ 4x²y²z² =8x2 y²z²(x+y+z)/ 4x²y²z²
= 2(x+y+z)
(iv)(x3 + 2x² + 3x) ÷ 2x =x(x2 +2x+3)/2x
=( x2 +2x+3)/2
(v)(p3q6 – p6q3) ÷ p3q3 = p3 q3(q3 - p3) / p3q3
=(q3 - p3)

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(2x + 1) (3x + 5) ÷ (2x + 1)
(ii) 26xy(x + 5) (y - 4) ÷ 13x(y - 4)
(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)
(iv) 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4)
(v) x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)
Answer
(i) 5(2x + 1) (3x + 5) ÷ (2x + 1)
=5(2x + 1) (3x + 5) / (2x + 1)
=5(3x+5)
(ii) 26xy(x + 5) (y - 4) ÷ 13x(y - 4)
=26xy(x + 5) (y - 4) / 13x(y - 4)
Cancelling 13x(y-4)
=2y(x+5)
(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)
=52pqr (p + q) (q + r) (r + p)/ 104pq(q + r) (r + p)
Cancelling 52pq(q + r) (r + p)
=r(p+q)/2
(iv)   20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4)
=4(y2 + 5y + 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 + 7y + 10) ÷  (y + 5)
(ii) (m2 - 14m - 32) ÷  (m + 2)
(iii) (5p2 - 25p + 20) ÷  (p - 1)
(iv) 4yz(z2 + 6z - 16) ÷ 2y(z + 8)
(v) 5pq(p2 - q2) ÷ 2p(p + q)
(vi) 12xy(9x2 - 16y2) ÷ 4xy(3x + 4y)
(vii) 39y3(50y2- 98) ÷ 26y2(5y+ 7)
Answer
(i)(y2 + 7y + 10) ÷  (y + 5)
=( y2 + 5y+2y + 10)/(y+5)
=[y(y+5)+2(y+5)] /(y+5)
=(y+1)(y+5) /(y+5)
=(y+1)
(ii) (m2 - 14m - 32) ÷  (m + 2)
= (m2 - 16m+2m - 32) / (m + 2)
=[m(m-16)+2(m-16)] /(m+2)
=(m+2)(m-16) /(m+2
=(m-16)
(iii) (5p2 - 25p + 20) ÷  (p - 1)
=5(p2-5p+4)/(p-1)
=5[p(p-1) -4(p-1)] /(p-1)
=5(p-1)(p-4)/(p-1)
=5(p-4)
(iv) 4yz(z2 + 6z - 16) ÷ 2y(z + 8)
=4yz[z2 -2z+8z-16]/ 2y(z + 8)
=4yz[z(z-2)+8(z-2)] / 2y(z + 8)
=4yz(z-2)(z+8) / 2y(z + 8)
=2z(z-2)
(v) 5pq(p2 - q2) ÷ 2p(p + q)
=5pq(p2 - q2) / 2p(p + q)
=5pq(p-q)(p+q) / 2p(p + q)
=5q(p-q)/2
(vi) 12xy(9x2 - 16y2) ÷ 4xy(3x + 4y)
=12xy(9x2 - 16y2) / 4xy(3x + 4y)
=12xy(3x+4y)(3x-4y) / 4xy(3x + 4y)
=3(3x-4y)
(vii) 39y3(50y2- 98) ÷ 26y2(5y+ 7)
=39y3(50y2- 98) /26y2(5y+ 7)
=78y3(25y2-49)/ 26y2(5y+ 7)
=3y(5y+7)(5y-7)/ (5y+ 7)
=3y(5y-7)

## Summary

1. 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
2. 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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