NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2: Introduction to Linear Polynomials

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.1 Solutions cover the basic ideas of polynomials from Introduction to Linear Polynomials. This exercise helps students identify the degree of a polynomial, write examples of polynomials of different degrees, and find coefficients and constant terms.

Chapter 2 begins with algebraic expressions and then focuses on one-variable polynomials. In Ganita Manjari Class 9 Chapter 2 Exercise 2.1, students practise terms, variables, coefficients, degree, constant polynomials, linear polynomials, quadratic polynomials and cubic polynomials. These Class 9 Maths Chapter 2 Exercise 2.1 Solutions explain each answer step by step in a simple, exam-ready format.

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.1 Solutions Structure 2026

Exercise 2.1 Question 1

Find the degrees of the following polynomials:

(i) 2x² − 5x + 3

Solution:

In the polynomial:

2x² − 5x + 3

the powers of x are:

• 2 in 2x²
• 1 in −5x
• 0 in the constant term 3

The highest power of x is 2.

Answer: The degree of 2x² − 5x + 3 is 2.

(ii) y³ + 2y − 1

Solution:

In the polynomial:

y³ + 2y − 1

the powers of y are:

• 3 in y³
• 1 in 2y
• 0 in the constant term −1

The highest power of y is 3.

Answer: The degree of y³ + 2y − 1 is 3.

(iii) −9

Solution:

The polynomial:

−9

is a non-zero constant polynomial.

A non-zero constant polynomial has degree 0.

Answer: The degree of −9 is 0.

(iv) 4z − 3

Solution:

In the polynomial:

4z − 3

the powers of z are:

• 1 in 4z
• 0 in the constant term −3

The highest power of z is 1.

Answer: The degree of 4z − 3 is 1.

Exercise 2.1 Question 2

Write polynomials of degrees 1, 2 and 3.

Solution:

A polynomial of degree 1 has the highest power of the variable equal to 1.
A polynomial of degree 2 has the highest power of the variable equal to 2.
A polynomial of degree 3 has the highest power of the variable equal to 3.

Examples:

Answer: Examples are 3x + 5, x² − 4x + 1 and 2x³ + x² − 7.

Exercise 2.1 Question 3

What are the coefficients of x² and x³ in the polynomial x⁴ − 3x³ + 6x² − 2x + 7?

Solution:

Given polynomial:

x⁴ − 3x³ + 6x² − 2x + 7

Now identify the required terms:

• The term containing x² is 6x².
• The coefficient of x² is 6.
• The term containing x³ is −3x³.
• The coefficient of x³ is −3.

Answer: The coefficient of x² is 6 and the coefficient of x³ is −3.

Exercise 2.1 Question 4

What is the coefficient of z in the polynomial 4z³ + 5z² − 11?

Solution:

Given polynomial:

4z³ + 5z² − 11

To find the coefficient of z, we look for the term containing z¹.

There is no z term in the polynomial.

So, the coefficient of z is 0.

Answer: The coefficient of z is 0.

Exercise 2.1 Question 5

What is the constant term of the polynomial 9x³ + 5x² − 8x − 10?

Solution:

Given polynomial:

9x³ + 5x² − 8x − 10

The constant term is the term without the variable.

Here, the term without x is:

−10

Answer: The constant term is −10.

Final Answers for Exercise 2.1

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2