RD Sharma Class 8 Solutions Chapter 8 - 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.