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Ncert Solutions for Class 8 Maths Chapter 14: Factorization Exercise 14.3





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 and comment at the end of the page.
Question 1
Carry out the following divisions.
(i) 28x4 ÷ 56x
 (ii) –36y³ ÷ 9y²
 (iii) 66pq²r3 ÷ 11qr²
 (iv) 34x3y3z3 ÷ 51xy²z3
(v) 12a8b8 ÷ (– 6a6b4)
Answer:
1) 28x4 ÷ 56x
= (2×2×7×x×x3  ) /( 2×2×2×7×x)
=x3/2
2) –36y³ ÷ 9y²
= (-2×2×3×3×y×y2 ) /( 3×3×y2)
=-4y
3) 66pq²r3 ÷ 11qr²
= 6pqr
4) 34x3y3z3 ÷ 51xy²z3
=(2/3) x2y
5) 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:
  1. (5x² – 6x) ÷ 3x =[x(5x-6)]  / 3x
    Cancelling x
    =(5x-6)/3
  2. (3y8 – 4y6 + 5y4) ÷ y4 = y4(3y4 -4y2 +5)/ y4
    =3y4-4y²+5
  3. 8(x3y²z² + x²y3z² + x²y²z3) ÷ 4x²y²z² =8x2 y²z²(x+y+z)/ 4x²y²z²
    = 2(x+y+z)
  4. (x3 + 2x² + 3x) ÷ 2x =x(x2 +2x+3)/2x
    =( x2 +2x+3)/2
  5. (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
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(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)

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Class 8 Maths Class 8 Science
Reference Books for class 8 Math

Given below are the links of some of the reference books for class 8 Math.

  1. Mathematics Foundation Course for JEE/Olympiad : Class 8 This book can take students maths skills further. Only buy if child is interested in Olympiad/JEE foundation courses.
  2. Mathematics for Class 8 by R S Aggarwal Detailed Mathematics book to clear basics and concepts. I would say it is a must have book for class 8 student.
  3. Pearson Foundation Series (IIT -JEE / NEET) Physics, Chemistry, Maths & Biology for Class 8 (Main Books) | PCMB Combo : These set of books could help your child if he aims to get extra knowledge of science and maths. These would be helpful if child wants to prepare for competitive exams like JEE/NEET. Only buy if you can provide help to the child while studying.
  4. Reasoning Olympiad Workbook - Class 8 :- Reasoning helps sharpen the mind of child. I would recommend students practicing reasoning even though they are not appearing for Olympiad.

You can use above books for extra knowledge and practicing different questions.







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