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# RD Sharma solutions for Class 8 Mathematics chapter 8 - Division of Algebraic Expressions

## Chapter 8: Division of Algebraic Expressions

Ex. 8.10Ex. 8.20Ex. 8.30Ex. 8.40Ex. 8.50Ex. 8.60

#### Chapter 8: Division of Algebraic Expressions Exercise 8.10 solutions [Page 2]

Ex. 8.10 | Q 1.1 | Page 2

Write the degree of each of the following polynomials.
2x2 + 5x2 − 7

Ex. 8.10 | Q 1.2 | Page 2

Write the degree of each of the following polynomials.
5x2 − 3x + 2

Ex. 8.10 | Q 1.3 | Page 2

Write the degree of each of the following polynomials.
2x + x2 − 8

Ex. 8.10 | Q 1.4 | Page 2

Write the degree of each of the following polynomials.

$\frac{1}{2} y^7 - 12 y^6 + 48 y^5 - 10$
Ex. 8.10 | Q 1.5 | Page 2

Write the degree of each of the following polynomials.

3x3 + 1
Ex. 8.10 | Q 1.6 | Page 2

Write the degree of each of the following polynomials.

5
Ex. 8.10 | Q 1.7 | Page 2

Write the degree of each of the following polynomials.

20x3 + 12x2y2 − 10y2 + 20
Ex. 8.10 | Q 2.1 | Page 2

Which of the following expressions are not polynomials?

x2 + 2x−2

Ex. 8.10 | Q 2.2 | Page 2

Which of the following expressions are not polynomials?

$\sqrt{ax} + x^2 - x^3$
Ex. 8.10 | Q 2.3 | Page 2

Which of the following expressions are not polynomials?

3y3 −$\sqrt{5}y$
Ex. 8.10 | Q 2.4 | Page 2

Which of the following expressions are not polynomials?

ax1/2 + ax + 9x2 + 4
Ex. 8.10 | Q 2.5 | Page 2

Which of the following expressions are not polynomials?

3x−2 + 2x−1 + 4x +5
Ex. 8.10 | Q 3.1 | Page 2

Write each of the following polynomials in the standard form. Also, write their degree.

x2 + 3 + 6x + 5x4

Ex. 8.10 | Q 3.2 | Page 2

Write each of the following polynomials in the standard form. Also, write their degree.

a2 + 4 + 5a6

Ex. 8.10 | Q 3.3 | Page 2

Write each of the following polynomials in the standard form. Also, write their degree.

(x3 − 1)(x3 − 4)

Ex. 8.10 | Q 3.4 | Page 2

Write each of the following polynomials in the standard form. Also, write their degree.

(y3 − 2)(y3 + 11)

Ex. 8.10 | Q 3.5 | Page 2

Write each of the following polynomials in the standard form. Also, write their degree.

$\left( a^3 - \frac{3}{8} \right)\left( a^3 + \frac{16}{17} \right)$
Ex. 8.10 | Q 3.6 | Page 2

Write each of the following polynomials in the standard form. Also, write their degree.

$\left( a + \frac{3}{4} \right)\left( a + \frac{4}{3} \right)$

#### Chapter 8: Division of Algebraic Expressions Exercise 8.20 solutions [Page 4]

Ex. 8.20 | Q 1 | Page 4

Divide 6x3y2z2 by 3x2yz.

Ex. 8.20 | Q 2 | Page 4

Divide 15m2n3 by 5m2n2.

Ex. 8.20 | Q 3 | Page 4

Divide 24a3b3 by −8ab.

Ex. 8.20 | Q 4 | Page 4

Divide −21abc2 by 7abc.

Ex. 8.20 | Q 5 | Page 4

Divide 72xyz2 by −9xz.

Ex. 8.20 | Q 6 | Page 4

Divide −72a4b5c8 by −9a2b2c3.

Ex. 8.20 | Q 7 | Page 4

Simplify:$\frac{16 m^3 y^2}{4 m^2 y}$

Ex. 8.20 | Q 8 | Page 4

Simplify:$\frac{32 m^2 n^3 p^2}{4mnp}$

#### Chapter 8: Division of Algebraic Expressions Exercise 8.30 solutions [Page 6]

Ex. 8.30 | Q 1 | Page 6

Divide x + 2x2 + 3x4 − x5 by 2x.

Ex. 8.30 | Q 2 | Page 6

Divide $y^4 - 3 y^3 + \frac{1}{2} y^2 by 3y$

Ex. 8.30 | Q 3 | Page 6

Divide −4a3 + 4a2 + a by 2a.

Ex. 8.30 | Q 4 | Page 6

Divide$- x^6 + 2 x^4 + 4 x^3 + 2 x^2\ \text{by} \sqrt{2} x^2$

Ex. 8.30 | Q 5 | Page 6

Divide 5z3 − 6z2 + 7z by 2z.

Ex. 8.30 | Q 6 | Page 6

Divide$\sqrt{3} a^4 + 2\sqrt{3} a^3 + 3 a^2 - 6a\ \text{by}\ 3a$

#### Chapter 8: Division of Algebraic Expressions Exercise 8.40 solutions [Pages 11 - 12]

Ex. 8.40 | Q 1 | Page 11

Divide 5x3 − 15x2 + 25x by 5x.

Ex. 8.40 | Q 2 | Page 11

Divide 4z3 + 6z2 − z by −$\frac{1}{2}$

Ex. 8.40 | Q 3 | Page 11

Divide 9x2y − 6xy + 12xy2 by −$\frac{3}{2}$

Ex. 8.40 | Q 4 | Page 11

Divide 3x3y2 + 2x2y + 15xy by 3xy.

Ex. 8.40 | Q 5 | Page 11

Divide x2 + 7x + 12 by x + 4.

Ex. 8.40 | Q 6 | Page 11

Divide 4y2 + 3y +$\frac{1}{2}$ by 2y + 1.

Ex. 8.40 | Q 7 | Page 11

Divide 3x3 + 4x2 + 5x + 18 by x + 2.

Ex. 8.40 | Q 8 | Page 11

Divide 14x2 − 53x + 45 by 7x − 9.

Ex. 8.40 | Q 9 | Page 11

Divide −21 + 71x − 31x2 − 24x3 by 3 − 8x.

Ex. 8.40 | Q 10 | Page 11

Divide 3y4 − 3y3 − 4y2 − 4y by y2 − 2y.

Ex. 8.40 | Q 11 | Page 11

Divide 2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1.

Ex. 8.40 | Q 12 | Page 11

Divide x4 − 2x3 + 2x2 + x + 4 by x2 + x + 1.

Ex. 8.40 | Q 13 | Page 11

Divide m3 − 14m2 + 37m − 26 by m2 − 12m +13.

Ex. 8.40 | Q 14 | Page 11

Divide x4 + x2 + 1 by x2 + x + 1.

Ex. 8.40 | Q 15 | Page 11

Divide x5 + x4 + x3 + x2 + x + 1 by x3 + 1.

Ex. 8.40 | Q 16 | Page 11

Divide 14x3 − 5x2 + 9x − 1 by 2x − 1 and find the quotient and remainder

Ex. 8.40 | Q 17 | Page 11

Divide 6x3 − x2 − 10x − 3 by 2x − 3 and find the quotient and remainder.

Ex. 8.40 | Q 18 | Page 11

Divide 6x3 + 11x2 − 39x − 65 by 3x2 + 13x + 13 and find the quotient and remainder.

Ex. 8.40 | Q 19 | Page 12

Divide 30x4 + 11x3 − 82x2 − 12x + 48 by 3x2 + 2x − 4 and find the quotient and remainder.

Ex. 8.40 | Q 20 | Page 12

Divide 9x4 − 4x2 + 4 by 3x2 − 4x + 2 and find the quotient and remainder.

Ex. 8.40 | Q 21.1 | Page 12

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
Ex. 8.40 | Q 21.2 | Page 12

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

 Dividend Divisor 15z3 − 20z2 + 13z − 12 3z − 6
Ex. 8.40 | Q 21.3 | Page 12

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

 Dividend Divisor 6y5 − 28y3 + 3y2 + 30y − 9 2y2 − 6
Ex. 8.40 | Q 21.4 | Page 12

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

 Dividend Divisor 34x − 22x3 − 12x4 − 10x2 − 75 3x + 7
Ex. 8.40 | Q 21.5 | Page 12

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

 Dividend Divisor 15y4 − 16y3 + 9y2 −$\frac{10}{3}$ y+6 3y − 2
Ex. 8.40 | Q 21.6 | Page 12

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

 Dividend Divisor 4y3 + 8y + 8y2 + 7 2y2 − y + 1
Ex. 8.40 | Q 21.7 | Page 12

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

 Dividend Divisor 6y5 + 4y4 + 4y3 + 7y2 + 27y + 6 2y3 + 1
Ex. 8.40 | Q 22 | Page 12

Divide 15y4 + 16y3 +$\frac{10}{3}$y − 9y2 − 6 by 3y − 2. Write down the coefficients of the terms in the quotient.

Ex. 8.40 | Q 23.1 | Page 12

Using division of polynomials, state whether

x + 6 is a factor of  x2 − x − 42

Ex. 8.40 | Q 23.2 | Page 12

Using division of polynomials, state whether

4x − 1 is a factor of 4x2 − 13x − 12

Ex. 8.40 | Q 23.3 | Page 12

Using division of polynomials, state whether

2y − 5 is a factor of 4y4 − 10y3 − 10y2 + 30y − 15

Ex. 8.40 | Q 23.4 | Page 12

Using division of polynomials, state whether

3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y − 35

Ex. 8.40 | Q 23.5 | Page 12

Using division of polynomials, state whether

z2 + 3 is a factor of z5 − 9z

Ex. 8.40 | Q 23.6 | Page 12

Using division of polynomials, state whether

2x2 − x + 3 is a factor of 6x5 − x4 + 4x3 − 5x2 − x − 15

Ex. 8.40 | Q 24 | Page 12

Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.

Ex. 8.40 | Q 25 | Page 12

What must be added to x4 + 2x3 − 2x2 + x − 1 , so that the resulting polynomial is exactly divisible by x2 + 2x − 3?

#### Chapter 8: Division of Algebraic Expressions Exercise 8.50 solutions [Page 15]

Ex. 8.50 | Q 1.1 | Page 15

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

3x2 + 4x + 5, x − 2

Ex. 8.50 | Q 1.2 | Page 15

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

10x2 − 7x + 8, 5x − 3

Ex. 8.50 | Q 1.3 | Page 15

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

5y3 − 6y2 + 6y − 1, 5y − 1

Ex. 8.50 | Q 1.4 | Page 15

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

x4 − x3 + 5xx − 1

Ex. 8.50 | Q 1.5 | Page 15

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

y4 + y2y2 − 2

Ex. 8.50 | Q 2.1 | Page 15

Find whether the first polynomial is a factor of the second.

x + 1, 2x2 + 5x + 4

Ex. 8.50 | Q 2.2 | Page 15

Find whether the first polynomial is a factor of the second.

y − 2, 3y3 + 5y2 + 5y + 2

Ex. 8.50 | Q 2.3 | Page 15

Find whether the first polynomial is a factor of the second.

4x2 − 5, 4x4 + 7x2 + 15

Ex. 8.50 | Q 2.4 | Page 15

Find whether the first polynomial is a factor of the second.

4 − z, 3z2 − 13z + 4

Ex. 8.50 | Q 2.5 | Page 15

Find whether the first polynomial is a factor of the second.

2a − 3, 10a2 − 9a − 5

Ex. 8.50 | Q 2.6 | Page 15

Find whether the first polynomial is a factor of the second.

4y + 1, 8y2 − 2y + 1

#### Chapter 8: Division of Algebraic Expressions Exercise 8.60 solutions [Page 17]

Ex. 8.60 | Q 1 | Page 17

Divide:
x2 − 5x + 6 by x − 3

Ex. 8.60 | Q 2 | Page 17

Divide:
ax2 − ay2 by ax + ay

Ex. 8.60 | Q 3 | Page 17

Divide:
x4 − y4 by x2 − y2

Ex. 8.60 | Q 4 | Page 17

Divide:
acx2 + (bc + ad)x + bd by (ax + b)

Ex. 8.60 | Q 5 | Page 17

Divide:

(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c

Ex. 8.60 | Q 6 | Page 17

Divide:

$\frac{1}{4} x^2 - \frac{1}{2}x - 12 by \frac{1}{2}x - 4$

## Chapter 8: Division of Algebraic Expressions

Ex. 8.10Ex. 8.20Ex. 8.30Ex. 8.40Ex. 8.50Ex. 8.60

## RD Sharma solutions for Class 8 Mathematics chapter 8 - Division of Algebraic Expressions

RD Sharma solutions for Class 8 Maths chapter 8 (Division of Algebraic Expressions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 8 Mathematics chapter 8 Division of Algebraic Expressions are Factors of Natural Numbers, Factors of Algebraic Expressions, Method of Common Factors, Factorisation by Regrouping Terms, Factorisation Using Identities, Factors of the Form ( x + a) ( x + b), Division of Algebraic Expressions - Division of a Monomial by Another Monomial, Division of Algebraic Expressions - Division of a Polynomial by a Monomial, Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial), Concept of Find the Error, Method of Completing the Square.

Using RD Sharma Class 8 solutions Division of Algebraic Expressions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer RD Sharma Textbook Solutions to score more in exam.

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