Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.1 Solutions: 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.

Key Takeaways

Polynomial Degree: The highest power of the variable gives the degree.
Constant Polynomial: A non-zero constant polynomial has degree 0.
Coefficient: The number multiplied by a variable term is its coefficient.
Missing Term: If a term is absent, its coefficient is 0.

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

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.1 Solutions

Exercise Set 2.1 is based on the definition of a polynomial and its degree. A one-variable polynomial is an algebraic expression involving one variable and its powers. The highest power of the variable in a polynomial is called its degree.

Examples:

• A polynomial of degree 1 is called a linear polynomial.
• A polynomial of degree 2 is called a quadratic polynomial.
• A polynomial of degree 3 is called a cubic polynomial.
• A non-zero constant polynomial has degree 0.

These Class 9 Maths polynomials exercise answers help students revise the first part of Chapter 2 before studying linear polynomials in detail.

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

Concept Used in Introduction to Linear Polynomials Exercise 2.1

Introduction to Linear Polynomials Exercise 2.1 uses the basic vocabulary of algebraic expressions and polynomials. Students need to identify terms, variables, coefficients, constants and degree.

Important points:

• A polynomial in one variable contains powers of one variable.
• The degree of a polynomial is the highest power of the variable.
• The coefficient is the number multiplied by a variable term.
• The constant term has no variable.
• A polynomial of degree 1 is a linear polynomial.
• A polynomial of degree 2 is a quadratic polynomial.
• A polynomial of degree 3 is a cubic polynomial.
• A non-zero constant polynomial has degree 0.

These ideas form the base of Class 9 Ganita Manjari linear polynomials solutions and help students understand later topics in Chapter 2.

About Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.1

Ganita Manjari Class 9 Chapter 2 Exercise 2.1 is the first exercise of the chapter Introduction to Linear Polynomials. It checks whether students can recognise the structure of a polynomial before moving to linear patterns, linear equations and graphs.

These Class 9 Maths Chapter 2 Exercise 2.1 Solutions prepare students for later topics such as:

• linear polynomials,
• quadratic polynomials,
• cubic polynomials,
• constant polynomials,
• degree of a polynomial,
• coefficients of terms,
• constant terms,
• evaluating polynomial values,
• linear patterns and linear relationships.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2