Short Intro

In this article, we provide complete step-by-step solutions for Exercise 2.1 from the chapter Introduction to Linear Polynomials for Class 9 Mathematics. These solutions will help students understand concepts like degree of polynomial, coefficients, variables, and constant terms in an easy way.

Quick Information Box

Topic	Details
Chapter Name	Introduction to Linear Polynomials
Exercise	Exercise 2.1
Class	Grade 9
Main Concepts	Polynomial, Degree, Coefficient, Constant
Difficulty Level	Easy
Best For	School Exams, Olympiads, Foundation Preparation

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Concepts Used (Topics Covered)

• Polynomial
• Degree of Polynomial
• Linear Polynomial
• Quadratic Polynomial
• Cubic Polynomial
• Coefficients
• Constant Term

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Important Formulas

Polynomial Degree Rule

The highest power of the variable in a polynomial is called its degree.

Examples

Linear Polynomial

$3x+7$

Degree = 1

Quadratic Polynomial

$x^2+5x+1$

Degree = 2

Cubic Polynomial

$5y^3+y^2+2y-1$

Degree = 3

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Exercise 2.1 – Step-by-Step Solutions

Question 1

Find the degrees of the following polynomials.

(i) $2x^2 – 5x + 3$

Solution

The powers of x are:

• $x^2$ → power = 2
• $x$ → power = 1
• Constant term → power = 0

Highest power = 2

Answer

Degree = 2

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(ii) $y^3 + 2y – 1$

Solution

The powers of y are:

• $y^3$ → power = 3
• $y$ → power = 1
• Constant → power = 0

Highest power = 3

Answer

Degree = 3

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(iii) $-9$

Solution

A constant polynomial has degree 0.

Answer

Degree = 0

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(iv) $4z – 3$

Solution

The highest power of z is 1.

Answer

Degree = 1

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Question 2

Write polynomials of degrees 1, 2 and 3.

Solution

Degree 1 Polynomial

$2x+5$

Degree 2 Polynomial

$x^2+3x+1$

Degree 3 Polynomial

$x^3+2x^2+4$

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Question 3

What are the coefficients of $x^2$x2 and $x^3$x3 in the polynomial
$x^4 – 3x^3 + 6x^2 – 2x + 7$

Solution

Given polynomial:

$x^4-3x^3+6x^2-2x+7$

• Coefficient of $x^2 = 6$
• Coefficient of $x^3 = -3$

Answer

• Coefficient of $x^2$ = 6
• Coefficient of $x^3$ = −3

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Question 4

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

Solution

There is no z-term in the polynomial.

Therefore, coefficient of z = 0.

Answer

Coefficient of z = 0

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Question 5

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

Solution

The constant term is the term without any variable.

Here, the constant term is:

$-10$

Answer

Constant term = −10

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Common Mistakes Students Make

• Confusing coefficient with degree.
• Forgetting that constant polynomials have degree 0.
• Writing coefficient of missing term incorrectly.
• Taking lowest power instead of highest power for degree.

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Exam Tips

✔ Degree = Highest power only
✔ Constant term has no variable
✔ Missing variable means coefficient = 0
✔ Read polynomial carefully before answering

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Practice MCQs

1. What is the degree of $7x^5 + 2x^2 – 1$?

A) 2
B) 3
C) 5
D) 1

Answer

✅ C) 5

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2. What is the coefficient of $x^2$ in $4x^2 + 7x – 3$?

A) 4
B) 7
C) -3
D) 2

Answer

✅ A) 4

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3. Which is a linear polynomial?

A) $x^2 + 1$
B) $2x + 5$
C) $x^3 – 7$
D) $x^4 + 2$

Answer

✅ B) $2x + 5$

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FAQ Section

Q1. What is a polynomial?

A polynomial is an algebraic expression made of variables, coefficients, and powers.

Q2. What is the degree of a polynomial?

The highest power of the variable is called the degree.

Q3. What is a linear polynomial?

A polynomial with degree 1 is called a linear polynomial.

Q4. What is a constant polynomial?

A polynomial having only a constant term is called a constant polynomial.

Q5. Can coefficient be negative?

Yes, coefficients can be positive or negative.

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