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RD Sharma Class 8 Solutions Chapter 8 - Division of Algebraic Expressions (Ex 8.1) Exercise 8.1

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RD Sharma Class 8 Solutions Chapter 8 - Division of Algebraic Expressions (Ex 8.1) Exercise 8.1 - Free PDF

Free PDF download of RD Sharma Class 8 Solutions Chapter 8 - Division of Algebraic Expressions Exercise 8.1 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 8 - Division of Algebraic Expressions Ex 8.1 Questions with Solutions for RD Sharma Class 8 Maths to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams.

Class 8 Chapter 8 RD Sharma Solutions - Division of Algebraic Expressions (Ex 8.1) Exercise 8.1

Introduction

RD Sharma Class 8 Chapter 8  Division of Algebraic Expressions is provided here. We have included real life-based questions based on the topic of Division of Algebraic Expressions to solve real-life problems. 

Some of the concepts which have been discussed in this chapter:

  • Polynomials and the degree of polynomials in two variables.

  • Division of a monomial by a monomial.

  • Division of a polynomial by a monomial.

  • Division of a polynomial by a binomial by using the long division method.

  • Division of polynomials by using factorization.


Polynomials and the degree of polynomials in two variables.

A polynomial can be defined as an expression including variables and coefficients, that includes only subtraction, addition, multiplication, and non-negative integer exponentiation of variables.

The degree of a polynomial is the highest power of a variable in the equation. The degree shows the highest power in the polynomial.

Let us understand this better with the aid of examples.

For example: 

\[7x^{4} + 8x^{_{3}}+ 3\] is a polynomial.  

Here,\[7x^{4},8x^{_{3}}\] and 3 are the terms. Here, \[7x^{4}\] is the leading term whereas 3 is a constant term. The coefficients of the polynomial here are 7 and 8.

The degree of the polynomial \[7x^{4} + 8x^{_{3}}+ 3\] is 4.

Let’s use another example: 

\[3x^{8}+ 4x^{3} + 7x + 1\]

The degree of the polynomial \[3x^{8}+ 4x^{3} + 7x + 1\] is 8.


Division of a Monomial by a Monomial.

In order to divide a monomial by a monomial,  we have to divide the numerical coefficients and then deduct the exponents of the same variables.


Division of a Polynomial by a Monomial.

In order to divide a polynomial by a monomial, we divide each term of the numerator by the denominator. We can also factorise the numerator by using the common factor method.


Division of a Polynomial By a Binomial By Using The Long Division Method.

In order to divide a polynomial by a binomial, we write the given polynomial in standard form. Then, we use the long division method, to divide the polynomial

.

Division of Polynomials by using Factorization.

We can divide polynomials using factorization too. In order to divide, we factor the numerator and/or the denominator. This helps simplify matters for us. Thus,we will be left with equivalent expressions that will be more comfortable to work with. 


Conclusion

For students wishing to score stellar marks in Maths, RD Sharma Solutions is the best study material. Students can easily access answers to the problems present in RD Sharma Class 8 Chapter 8  by downloading the PDF. It contains all solutions in a detailed manner and also expects questions to be asked in the exam. Students will get more confident about the exam after solving these problems.

FAQs on RD Sharma Class 8 Solutions Chapter 8 - Division of Algebraic Expressions (Ex 8.1) Exercise 8.1

1. What are the topics discussed in this chapter?

Some of the topics which discussed in the chapter are:

  • Polynomials and the degree of polynomials in two variables.

  • Division of a monomial by a monomial.

  • Division of a polynomial by a monomial.

  • Division of a polynomial by a binomial by using the long division method.

  • Division of polynomials by using factorization.

Here, students will learn the meaning and the concept of the Division of Algebraic Expressions.

2. What is the degree of a polynomial?

In the chapter Division of Algebraic Expressions, students often get confused as to what the degree of a polynomial actually means. It is very important to clear doubts otherwise they can lead to confusion while solving questions.


The value of the highest exponential power of a polynomial is called the degree of a polynomial.


Thus, the degree of a polynomial is the highest power of one of the terms of a polynomial which has the highest power.

3. What is a polynomial?

A polynomial can be easily described as:

An expression that contains variables and coefficients, which include only subtraction, addition, multiplication, and non-negative integer exponentiation of variables, is defined as a polynomial.

A polynomial is made up of terms that are related to each other by mathematical operations such as addition or subtraction. 

Our subject matter experts at Vedantu have prepared the RD Sharma solutions to aid the students who are finding difficulties in solving them. 

4. Are the solutions to Division of Algebraic Expressions free?

Yes, the RD Sharma Class 8 Solutions Chapter 8 - Division of Algebraic Expressions are absolutely free. Students usually have doubts while solving RD Sharma Class. Our experts have carefully made the solutions keeping in mind the difficulties students face while solving RD Sharma Class 8. The solutions are easy to understand. Students can easily download the RD Sharma Class 8 Solutions Chapter 8 - Division of Algebraic Expressions which are provided in PDF format.