#### Chapters

Chapter 2: Powers

Chapter 3: Squares and Square Roots

Chapter 4: Cubes and Cube Roots

Chapter 5: Playing with Numbers

Chapter 6: Algebraic Expressions and Identities

Chapter 7: Factorization

Chapter 8: Division of Algebraic Expressions

Chapter 9: Linear Equation in One Variable

Chapter 10: Direct and Inverse Variations

Chapter 11: Time and Work

Chapter 12: Percentage

Chapter 13: Proft, Loss, Discount and Value Added Tax (VAT)

Chapter 14: Compound Interest

Chapter 15: Understanding Shapes-I (Polygons)

Chapter 16: Understanding Shapes-II (Quadrilaterals)

Chapter 17: Understanding Shapes-III (Special Types of Quadrilaterals)

Chapter 18: Practical Geometry (Constructions)

Chapter 19: Visualising Shapes

Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)

Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Chapter 23: Data Handling-I (Classification and Tabulation of Data)

Chapter 24: Data Handling-II (Graphical Representation of Data as Histograms)

Chapter 25: Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

Chapter 26: Data Handling-IV (Probability)

Chapter 27: Introduction to Graphs

#### RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

## Chapter 8: Division of Algebraic Expressions

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

Write the degree of each of the following polynomials.

2*x*^{2} + 5*x*^{2} − 7

Write the degree of each of the following polynomials.

5*x*^{2} − 3*x* + 2

Write the degree of each of the following polynomials.

2*x* + *x*^{2} − 8

Write the degree of each of the following polynomials.

Write the degree of each of the following polynomials.

*x*

^{3}+ 1

Write the degree of each of the following polynomials.

Write the degree of each of the following polynomials.

*x*

^{3}+ 12

*x*

^{2}

*y*

^{2}− 10

*y*

^{2}+ 20

Which of the following expressions are not polynomials?

*x*^{2} + 2*x*^{−2}

Which of the following expressions are not polynomials?

Which of the following expressions are not polynomials?

*y*

^{3}−\[\sqrt{5}y\]

Which of the following expressions are not polynomials?

*ax*

^{1/2}+ a

*x*+ 9

*x*

^{2}+ 4

Which of the following expressions are not polynomials?

*x*

^{−2}+ 2

*x*

^{−1}+ 4

*x*+5

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

*x*^{2} + 3 + 6*x* + 5*x*^{4}

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

* **a*^{2} + 4 + 5*a*^{6}

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

(*x*^{3} − 1)(*x*^{3} − 4)

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

(*y*^{3}^{ }− 2)(*y*^{3}^{ }+ 11)

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

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

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

Divide 6*x*^{3}*y*^{2}*z*^{2} by 3*x*^{2}*yz*.

Divide 15*m*^{2}*n*^{3} by 5*m*^{2}*n*^{2}.

Divide 24*a*^{3}*b*^{3} by −8ab.

Divide −21*abc*^{2} by 7*abc*.

Divide 72*xyz*^{2} by −9*xz*.

Divide −72*a*^{4}*b*^{5}*c*^{8} by −9*a*^{2}*b*^{2}*c*^{3}.

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

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

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

Divide *x* + 2*x*^{2} + 3*x*^{4} − *x*^{5} by 2*x*.

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

Divide −4*a*^{3} + 4*a*^{2} + *a* by 2*a**.*

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

Divide 5*z*^{3} − 6*z*^{2} + 7*z* by 2*z*.

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]

Divide 5*x*^{3} − 15*x*^{2} + 25*x* by 5*x**.*

Divide 4*z*^{3} + 6*z*^{2} − *z* by −\[\frac{1}{2}\]

Divide 9*x*^{2}*y* − 6*xy* + 12*xy*^{2} by −\[\frac{3}{2}\]

Divide 3*x*^{3}*y*^{2} + 2*x*^{2}*y* + 15*xy* by 3*xy**.*

Divide *x*^{2} + 7*x* + 12 by *x* + 4.

Divide 4*y*^{2} + 3*y* +\[\frac{1}{2}\] by 2*y* + 1.

Divide 3*x*^{3} + 4*x*^{2} + 5*x* + 18 by *x* + 2.

Divide 14*x*^{2} − 53*x* + 45 by 7*x* − 9.

Divide −21 + 71*x* − 31*x*^{2} − 24*x*^{3} by 3 − 8*x**.*

Divide 3*y*^{4} − 3y^{3} − 4*y*^{2} − 4*y* by *y*^{2} − 2*y**.*

Divide 2*y*^{5} + 10*y*^{4} + 6*y*^{3} + *y*^{2} + 5*y* + 3 by 2*y*^{3} + 1.

Divide *x*^{4} − 2*x*^{3} + 2*x*^{2} + *x* + 4 by *x*^{2} +* x* + 1.

Divide *m*^{3} − 14*m*^{2} + 37*m* − 26 by *m*^{2} − 12*m* +13.

Divide *x*^{4} + *x*^{2} + 1 by *x*^{2} + *x* + 1.

Divide *x*^{5} + *x*^{4} + *x*^{3} + *x*^{2} + *x* + 1 by *x*^{3} + 1.

Divide 14*x*^{3} − 5*x*^{2} + 9*x* − 1 by 2*x* − 1 and find the quotient and remainder

Divide 6*x*^{3} − *x*^{2} − 10*x* − 3 by 2*x* − 3 and find the quotient and remainder.

Divide 6*x*^{3}^{ }+ 11*x*^{2} − 39*x* − 65 by 3*x*^{2} + 13*x* + 13 and find the quotient and remainder.

Divide 30*x*^{4} + 11*x*^{3} − 82*x*^{2} − 12*x* + 48 by 3*x*^{2} + 2*x* − 4 and find the quotient and remainder.

Divide 9*x*^{4} − 4*x*^{2} + 4 by 3*x*^{2} − 4*x* + 2 and find the quotient and remainder.

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

Dividend | Divisor |

14x^{2} + 13x − 15 |
7x − 4 |

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

Dividend | Divisor |

15z^{3} − 20z^{2} + 13z − 12 |
3z − 6 |

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

Dividend | Divisor |

6y^{5} − 28y^{3} + 3y^{2} + 30y − 9 |
2y^{2} − 6 |

Dividend | Divisor |

34x − 22x^{3} − 12x^{4} − 10x^{2} − 75 |
3x + 7 |

Dividend | Divisor |

15y^{4} − 16y^{3} + 9y2 −\[\frac{10}{3}\] y+6 |
3y − 2 |

Dividend | Divisor |

4y^{3} + 8y + 8y^{2} + 7 |
2y^{2} − y + 1 |

Dividend | Divisor |

6y^{5} + 4y^{4} + 4y^{3} + 7y^{2} + 27y + 6 |
2y^{3} + 1 |

Divide 15*y*^{4} + 16*y*^{3} +\[\frac{10}{3}\]*y* − 9*y*^{2} − 6 by 3*y* − 2. Write down the coefficients of the terms in the quotient.

Using division of polynomials, state whether

*x* + 6 is a factor of *x*^{2} − *x* − 42

Using division of polynomials, state whether

4*x* − 1 is a factor of 4*x*^{2} − 13*x* − 12

Using division of polynomials, state whether

2*y* − 5 is a factor of 4*y*^{4} − 10*y*^{3} − 10*y*^{2} + 30*y* − 15

Using division of polynomials, state whether

3*y*^{2} + 5 is a factor of 6*y*^{5} + 15*y*^{4} + 16*y*^{3} + 4*y*^{2} + 10*y* − 35

Using division of polynomials, state whether

*z*^{2}^{ }+ 3 is a factor of *z*^{5} − 9*z*

Using division of polynomials, state whether

2*x*^{2} − *x* + 3 is a factor of 6*x*^{5} − *x*^{4} + 4*x*^{3} − 5*x*^{2} − *x* − 15

Find the value of *a*, if *x* + 2 is a factor of 4*x*^{4} + 2*x*^{3} − 3*x*^{2} + 8*x* + 5*a*.

What must be added to *x*^{4} + 2*x*^{3} − 2*x*^{2} + *x* − 1 , so that the resulting polynomial is exactly divisible by *x*^{2}^{ }+ 2x − 3?

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

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

3*x*^{2} + 4*x* + 5, *x* − 2

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

10*x*^{2} − 7*x* + 8, 5*x* − 3

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

5*y*^{3} − 6*y*^{2} + 6*y* − 1, 5*y* − 1

*x*^{4} − *x*^{3} + 5*x*, *x* − 1

*y*^{4} + *y*^{2}, *y*^{2} − 2

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

*x* + 1, 2*x*^{2} + 5*x* + 4

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

*y* − 2, 3*y*^{3} + 5*y*^{2} + 5*y* + 2

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

4*x*^{2} − 5, 4*x*^{4} + 7*x*^{2} + 15

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

4 − *z*, 3*z*^{2} − 13*z* + 4

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

2*a* − 3, 10*a*^{2} − 9*a* − 5

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

4*y* + 1, 8*y*^{2} − 2*y* + 1

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

*Divide:**x*^{2} − 5*x* + 6 by *x* − 3

*Divide:**ax*^{2} − *ay*^{2} by *ax + ay*

*Divide:**x*^{4} − *y*^{4} by *x*^{2} − *y*^{2}

*Divide:**acx*^{2} + (*bc + ad*)*x + bd* by (*ax + b*)

*Divide:*

(*a*^{2} + 2*ab* + *b*^{2}) − (*a*^{2} + 2*ac* + *c*^{2}) by 2*a* + *b* + *c*

*Divide:*

## Chapter 8: Division of Algebraic Expressions

#### RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

#### Textbook solutions for Class 8

## 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 รท Polynomial), Concept of Find the Error, Method of Completing the Square.

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