RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev

The document RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8

Question 1: Divide x + 2x2 + 3x4x5 by 2x.
Answer 1: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 2: Divide y43y3+1/2 y2 by 3yy4-3y3+12y2 by 3y.
Answer 2:

 RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev

Question 3: Divide −4a3 + 4a2 + a by 2a.
Answer 3: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
=2a2+2a+1/2
Question 4: Divide x6+2x4+4x3+2x2 byRD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Answer 4:

 RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev 

Question 5: Divide 5z3 − 6z2 + 7z by 2z.
Answer 5: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 6: Divide RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev+3a26a by 3a3 a4+23 a3+3a2-6a by 3a.
Answer 6:

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev

Question 7: Divide 5x3 − 15x2 + 25x by 5x.
Answer 7: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 8: Divide 4z3 + 6z2z by −1/2 12z.
Answer 8: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev

Question 9: Divide 9x2y − 6xy + 12xy2 by −3/2 32xy.
Answer 9: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 10: Divide 3x3y2 + 2x2y + 15xy by 3xy.

Answer 10:

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 11: Divide x2 + 7x + 12 by x + 4.
Answer 11:

 RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev

Question 12: Divide 4y2 + 3y + 1/212 by 2y + 1.
Answer 12:

 RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 13: Divide 3x3 + 4x2 + 5x + 18 by x + 2.
Answer 13: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 14: Divide 14x2 − 53x + 45 by 7x − 9.
Answer 14: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 15: Divide −21 + 71x − 31x2 − 24x3 by 3 − 8x.
Answer 15: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 16: Divide 3y4 − 3y3 − 4y2 − 4y by y2 − 2y.
Answer 16: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 17: Divide 2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1.
Answer 17: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 18: Divide x4 − 2x3 + 2x2 + x + 4 by x2 + x + 1.
Answer 18: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 19: Divide m3 − 14m2 + 37m − 26 by m2 − 12m +13.
Answer 19:

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 20: Divide x4 + x2 + 1 by x2 + x + 1.
Answer 20: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 21: Divide x5 + x4 + x3 + x2 + x + 1 by x3 + 1.
Answer 21: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 22: Divide 14x3 − 5x2 + 9x − 1 by 2x − 1 and find the quotient and remainder
Answer 22: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRevQuotient = 7x2 + x + 5Remainder = 4

Question 23: Divide 6x3x2 − 10x − 3 by 2x − 3 and find the quotient and remainder.
Answer 23: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Quotient = 3x2+ 4x + 1 Remainder = 0Question 24: Divide 6x3 + 11x2 − 39x − 65 by 3x2 + 13x + 13 and find the quotient and remainder.
Answer 24: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev 

Quotient = 2x5Remainder =

Question 25: Divide 30x4 + 11x3 − 82x2 − 12x + 48 by 3x2 + 2x − 4 and find the quotient and remainder.
Answer 25: Quotient =10x23x12 

Remainder= 0 
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Question 26: Divide 9x4 − 4x2 + 4 by 3x2 − 4x + 2 and find the quotient and remainder.
Answer 26: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Quotient = 3x2 + 4x + 2 and remainder = 0.
Question 27: Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

Dividend 
Divisor 
14x2 + 13x − 15 
7x − 4 
15z3 − 20z2 + 13z − 12 
3z − 6 
6y5 − 28y3 + 3y2 + 30y − 9 
2y2 − 6 
34x − 22x3 − 12x4 − 10x2 − 75 
3x + 7 
15y4 − 16y3 + 9y2 − 10/3 103y + 6 
3y − 2 
4y3 + 8y + 8y2 + 7 
2y2 − y + 1 
6y5 + 4y4 + 4y3 + 7y2 + 27y + 6 
2y3 + 1 

Answer 27: (i) 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Quotient = 2x + 3
Remainder = -3
Divisor = 7x - 4
Divisor ×× Quotient + Remainder = (7x - 4) (2x + 3) - 3  

= 14x+ 21- 8- 12 - 3 
= 14x2 + 13x - 15
= Dividend 

Thus,
Divisor ×× Quotient + Remainder = Dividend
Hence verified. 

(ii) 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Quotient = 5z2+10/3 z+11Remainder = 54Divisor = 3z6Divisor × Quotient +Remainder = (3z6)( 5z2+10/3 z+11)+54= 15z3+10z2+33z30z220z66+54 

= 15z320z2+13z12 

= Dividend 
Thus,Divisor × Quotient + Remainder = DividendHence verified. 
(iii) 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev  
Quotient = 3y35y+323y3-5y+32
Remainder = 0
Divisor = 2y2 - 6
Divisor ×× Quotient + Remainder =
(2y26) (3y35y+32)+0=6y510y3+3y218y3+30y9=6y528 y3+3y2+30y9 = Dividend 

Thus, Divisor ×× Quotient + Remainder = Dividend
Hence verified. 

(iv) 
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Quotient  = - 4x3 + 2x2 - 8x + 30
Remainder  = - 285 
Divisor  = 3x + 7
Divisor ×× Quotient + Remainder =  (3x + 7) (- 4x3 + 2x2 - 8x + 30) - 285 

- 12x4 + 6x3 - 24x2 + 90- 28x3 + 14x2 - 56x + 210 - 285
- 12x 4 - 22x3 - 10x2 + 34x - 75
=  Dividend

Thus,
Divisor ×× Quotient + Remainder = Dividend
Hence verified. 

(v)  
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Quotient =  5y32y2+5/3 y5y3-2y2+53y
Remainder =  6
Divisor = 3y - 2
Divisor ×× Quotient  + Remainder = (3y - 2) (5y3 - 2y2 + 5/3 y53y) + 6

15y46y3+5y210y3+4y210/3 y+615y4-6y3+5y2-10y3+4y2-103y+6
15y416y3+9y210/3 y+615y4-16y3+9y2-103y+6
 =  Dividend 
 

Thus,
Divisor ×× Quotient + Remainder = Dividend
Hence verified. 

(vi) 
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-2) Class 8 Notes | EduRev
Quotient =  2y + 5
Remainder =  11y + 2
Divisor =  2y2 - y + 1
Divisor ×× Quotient + Remainder =  (2y2 - y + 1) (2y + 5) + 11y + 2 

=  4y3 +10y2 - 2y2