---
title: "NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1"
url: https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-1
dateModified: 2026-10-07T15:41:27+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1

Chapter 2: Introduction to Linear Polynomials. Every question from Exercise 2.1, with full working and the final answer.

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## Exercise Set 2.1

### Question 1

*4 marks · Short answer*

Find the degrees of the following polynomials: 
(i) $2x^2 – 5x + 3$
(ii) $y^3 + 2y – 1$
(iii) $–9$
(iv) $4z – 3$

**Part (i)**

1. The highest power of the variable x in $2x^2 - 5x + 3$ is 2.
2. Therefore, the degree of the polynomial is 2.

Answer (i): 2

**Part (ii)**

1. The highest power of the variable y in $y^3 + 2y - 1$ is 3.
2. Therefore, the degree of the polynomial is 3.

Answer (ii): 3

**Part (iii)**

1. The constant polynomial $-9$ can be written as $-9x^0$.
2. Therefore, the degree of the polynomial is 0.

Answer (iii): 0

**Part (iv)**

1. The highest power of the variable z in $4z - 3$ is 1.
2. Therefore, the degree of the polynomial is 1.

Answer (iv): 1

**Answer:** The degrees are (i) 2, (ii) 3, (iii) 0, (iv) 1.

> Common mistake: Confusing the coefficient of the leading term with the degree of the polynomial.

### Question 2

*3 marks · Short answer*

Write polynomials of degrees 1, 2 and 3.

**Solution**

1. A polynomial of degree 1 is a linear polynomial, for example, $x + 1$.
2. A polynomial of degree 2 is a quadratic polynomial, for example, $x^2 + 2x + 1$.
3. A polynomial of degree 3 is a cubic polynomial, for example, $x^3 + 1$. (Answers may vary as any valid polynomial of the respective degree is correct).

**Answer:** Degree 1: $x + 1$, Degree 2: $x^2 + 2x + 1$, Degree 3: $x^3 + 1$

> Common mistake: Writing an expression that is not a polynomial, such as having a variable in the denominator or with a fractional exponent.

### Question 3

*3 marks · Short answer*

What are the coefficients of $x^2$ and $x^3$ in the polynomial $x^4 – 3x^3 + 6x^2 – 2x + 7$?

**Solution**

1. The given polynomial is $x^4 - 3x^3 + 6x^2 - 2x + 7$.
2. The term containing $x^2$ is $6x^2$, so its coefficient is 6.
3. The term containing $x^3$ is $-3x^3$, so its coefficient is $-3$.

**Answer:** Coefficient of $x^2$ is 6 and coefficient of $x^3$ is $-3$.

> Common mistake: Forgetting to include the negative sign when writing the coefficient of $x^3$.

### Question 4

*2 marks · Very short answer*

What is the coefficient of $z$ in the polynomial $4z^3 + 5z^2 – 11$?

**Solution**

1. The given polynomial is $4z^3 + 5z^2 - 11$.
2. Since the term with variable $z$ (i.e., $z^1$) is absent, it can be written as $0z$.
3. Therefore, the coefficient of $z$ is 0.

**Answer:** 0

> Common mistake: Writing the coefficient of $z^2$ or $z^3$ instead of $z$.

### Question 5

*2 marks · Very short answer*

What is the constant term of the polynomial $9x^3 + 5x^2 – 8x – 10$?

**Solution**

1. The given polynomial is $9x^3 + 5x^2 - 8x - 10$.
2. The constant term is the term independent of the variable x.
3. Therefore, the constant term is $-10$.

**Answer:** -10

> Common mistake: Omitting the negative sign from the constant term.

## Related pages

- [All Chapter 2 NCERT solutions](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions)
- [Exercise 2.2](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-2)
- [Exercise 2.3](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-3)
- [Exercise 2.4](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-4)
- [Exercise 2.5](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-5)
- [Exercise 2.6](https://www.swavid.com/maths/class/9/chapter/introduction-to-linear-polynomials/ncert-solutions/exercise-2-6)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student