RD Sharma Solutions for Class 8 Chapter 8 Division of Algebraic Expressions Exercise 8.1

In this chapter, we provide RD Sharma Solutions for Class 8 Chapter 8 Division of Algebraic Expressions Exercise 8.1 for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 8 Chapter 8 Division of Algebraic Expressions Exercise 8.1 pdf, free RD Sharma Solutions for Class 8 Chapter 8 Division of Algebraic Expressions Exercise 8.1 book pdf download. Now you will get step by step solution to each question.

Access Answers to RD Sharma Solutions for Class 8 Maths Exercise 8.1 Chapter 8 Division of Algebraic Expressions

EXERCISE 8.1 PAGE NO: 8.2

1. Write the degree of each of the following polynomials:

(i) 2x3 + 5x2 – 7

(ii) 5x2 – 3x + 2

(iii) 2x + x2 – 8

(iv) 1/2y7 – 12y6 + 48y5 – 10

(v) 3x3 + 1

(vi) 5

(vii) 20x3 + 12x2y2 – 10y2 + 20

Solution:

(i) 2x3 + 5x2 – 7

We know that in a polynomial, degree is the highest power of the variable.

The degree of the polynomial, 2x3 + 5x2 – 7 is 3.

(ii) 5x2 – 3x + 2

The degree of the polynomial, 5x2 – 3x + 2 is 2.

(iii) 2x + x2 – 8

The degree of the polynomial, 2x + x2 – 8 is 2.

(iv) 1/2y7 – 12y6 + 48y5 – 10

The degree of the polynomial, 1/2y7 – 12y6 + 48y5 – 10 is 7.

(v) 3x3 + 1

The degree of the polynomial, 3x3 + 1 is 3

(vi) 5

The degree of the polynomial, 5 is 0 (since 5 is a constant number).

(vii) 20x3 + 12x2y2 – 10y2 + 20

The degree of the polynomial, 20x3 + 12x2y2 – 10y2 + 20 is 4.

2. Which of the following expressions are not polynomials?

(i) x2 + 2x-2

(ii) √(ax) + x2 – x3

(iii) 3y3 – √5y + 9

(iv) ax1/2 + ax + 9x2 + 4

(v) 3x-3 + 2x-1 + 4x + 5

Solution:

(i) x2 + 2x-2

The given expression is not a polynomial.

Because a polynomial does not contain any negative powers or fractions.

(ii) √(ax) + x2 – x3

The given expression is a polynomial.

Because the polynomial has positive powers.

(iii) 3y3 – √5y + 9

The given expression is a polynomial.

Because the polynomial has positive powers.

(iv) ax1/2 + ax + 9x2 + 4

The given expression is not a polynomial.

Because a polynomial does not contain any negative powers or fractions.

(v) 3x-3 + 2x-1 + 4x + 5

The given expression is not a polynomial.

Because a polynomial does not contain any negative powers or fractions.

3. Write each of the following polynomials in the standard from. Also, write their degree:

(i) x2 + 3 + 6x + 5x4

(ii) a2 + 4 + 5a6

(iii) (x3 – 1) (x3 – 4)

(iv) (y3 – 2) (y3 + 11)

(v) (a3 – 3/8) (a3 + 16/17)

(vi) (a + 3/4) (a + 4/3)

Solution:

(i) x2 + 3 + 6x + 5x4

The standard form of the polynomial is written in either increasing or decreasing order of their powers.

3 + 6x + x2 + 5x4 or 5x4 + x2 + 6x + 3

The degree of the given polynomial is 4.

(ii) a2 + 4 + 5a6

The standard form of the polynomial is written in either increasing or decreasing order of their powers.

4 + a2 + 5a6 or 5a6 + a2 + 4

The degree of the given polynomial is 6.

(iii) (x3 – 1) (x3 – 4)

x6 – 4x3 – x3 + 4

x6 – 5x3 + 4

The standard form of the polynomial is written in either increasing or decreasing order of their powers.

x6 – 5x3 + 4 or 4 – 5x3 + x6

The degree of the given polynomial is 6.

(iv) (y3 – 2) (y3 + 11)

y6 + 11y3 – 2y3 – 22

y6 + 9y3 – 22

The standard form of the polynomial is written in either increasing or decreasing order of their powers.

y6 + 9y3 – 22 or -22 + 9y3 + y6

The degree of the given polynomial is 6.

(v) (a3 – 3/8) (a3 + 16/17)

a6 + 16a3/17 – 3a3/8 – 6/17

a6 + 77/136a3 – 48/136

The standard form of the polynomial is written in either increasing or decreasing order of their powers.

a6 + 77/136a3 – 48/136 or -48/136 + 77/136a3 + a6

The degree of the given polynomial is 6.

(vi) (a + 3/4) (a + 4/3)

a2 + 4a/3 + 3a/4 + 1

a2 + 25a/12 + 1

The standard form of the polynomial is written in either increasing or decreasing order of their powers.

a2 + 25a/12 + 1 or 1 + 25a/12 + a2

The degree of the given polynomial is 2.

All Chapter RD Sharma Solutions For Class 8 Maths

*************************************************

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also share ncertsolutionsfor.com to your friends.

Leave a Comment

Your email address will not be published.