NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1 (2026-27)

Question 1.
Find the degrees of the following polynomials.

(i) 2x² – 5x + 3

Solution:
In the polynomial 2x² – 5x + 3, the highest power of the variable x is 2. Therefore, the degree of the polynomial is 2.

(ii) y³ + 2y – 1

Solution:
In the polynomial y³ + 2y – 1, the highest power of the variable y is 3. Therefore, the degree of the polynomial is 3.

(iii) – 9

Solution:
The polynomial -9 is a constant polynomial. A non-zero constant polynomial has degree 0. Therefore, the degree of -9 is 0.

(iv) 4z – 3

Solution:
In the polynomial 4z – 3, the highest power of the variable z is 1. Therefore, the degree of the polynomial is 1.

Question 2.
Write the polynomials of degree 1, 2, and 3.

Solution:
Degree 1 polynomial: 4x + 2
Degree 2 polynomial: 3x² - 4x + 7
Degree 3 polynomial: x³ + 2x² - x + 10

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

Solution:
In the polynomial x⁴ – 3x³ + 6x² – 2x + 7, the term containing x² is 6x². So, the coefficient of x² is 6. The term containing x³ is -3x³. So, the coefficient of x³ is -3.

Question 4.
What is the coefficient of z in the polynomial 4z³ + 5z² – 11?

Solution:
The polynomial 4z³ + 5z² – 11 does not contain any z term. We can write it as 4z³ + 5z² + 0z – 11. Therefore, the coefficient of z is 0.

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

Solution:
In the polynomial 9x³ + 5x² – 8x – 10, the term without any variable is -10. Therefore, the constant term is -10.

Think and Reflect (NCERT Textbook Page No. 17)

Question 1.
Can you identify the terms, variables, and coefficients of this algebraic expression?

Solution:
The given algebraic expression is 200l + 160w + 50lw.

Terms: 200l, 160w and 50lw
Variables: l and w
Coefficients: The coefficient of l is 200, the coefficient of w is 160, and the coefficient of lw is 50.

Question 2.
How is it different from the algebraic expression in Example 1?

Solution:
The expression in Example 1 is 4x + 5y + 3, which is a linear polynomial in the variables x and y. The expression 200l + 160w + 50lw has variables l and w, but it is not a linear polynomial because it includes the product term lw.

Think and Reflect (NCERT Textbook Page No. 17)

Question 1.
Can you identify the terms, variables, and coefficients of this algebraic expression?

Solution:
The given algebraic expression is 10x - x².

Terms: 10x and -x²
Variable: x
Coefficients: The coefficient of x is 10, and the coefficient of x² is -1.

Question 2.
Can you point out any similarity or difference between the algebraic expressions obtained in Examples 1 and 3?

Solution:
Similarity: Both expressions contain variables.

Difference: The expression in Example 1, 4x + 5y + 3, is a linear polynomial in x and y. The expression in Example 3, 10x - x², is not linear because it contains x². It is a quadratic expression in the variable x.

Key Takeaways from Vedantu’s Ganita Manjari Class 9 Exercise 2.1

• Identify the degree of a polynomial by finding its highest power.

• Write examples of polynomials with degrees 1, 2, and 3.

• Find the coefficient of a specific variable or term.

• Identify the constant term in a polynomial.

• Recognise the terms, variables, and coefficients in an algebraic expression.

• Understand the difference between linear and non-linear expressions.

• Identify why terms such as lw or x² affect whether an expression is linear.

Access Exercise Wise NCERT Solutions for Chapter 2 Maths Class 9

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