Get complete step-by-step Class 9 Maths Chapter 2 Exercise 2.1 Solutions from the new NCERT Ganita Manjari (2026). These solutions explain degree of polynomial, coefficients and constant terms in a simple CBSE exam-oriented manner.
📌 Quick Information
- Chapter: Introduction to Linear Polynomials
- Class: 9
- Board: CBSE
- Book: Ganita Manjari 2026
- Exercise: 2.1
📚 Exercise 2.1 Contents
About Class 9 Maths Chapter 2
Chapter 2 introduces students to polynomials, degree of polynomials, coefficients and constant terms. This chapter forms the foundation of algebra and higher mathematics. we are providing the Class 9 Maths Chapter 2 Exercise 2.1 Solutions.
Important Topics Covered
- Polynomial
- Degree of Polynomial
- Coefficient
- Constant Term
- Linear Polynomial
- Quadratic Polynomial
- Cubic Polynomial
📝 Class 9 Maths Chapter 2 Exercise 2.1 Solutions
Q1. Find the degree of the following polynomials
(i) 2x²−5x+3
Highest power of x = 2
Degree = 2
(ii) y³+2y−1
Highest power of y = 3
Degree = 3
(iii) −9
Constant polynomial
Degree = 0
(iv) 4z−3
Highest power = 1
Degree = 1
- 2
- 3
- 0
- 1
💡 Key Concept: Degree = highest exponent.
⚠️ Common Mistake: Constant polynomial has degree 0.
🎯 Exam Tip: Always identify the highest power.
Q2. Write polynomials of degrees 1, 2 and 3.
Given:
Required degrees are 1, 2 and 3.
To Find:
Examples of polynomials having degrees 1, 2 and 3.
Solution:
A polynomial of degree 1 is called a linear polynomial.
3x + 5
A polynomial of degree 2 is called a quadratic polynomial.
x2 + 2x + 1
A polynomial of degree 3 is called a cubic polynomial.
2x3 − x + 4
- Degree 1 : 3x + 5
- Degree 2 : x² + 2x + 1
- Degree 3 : 2x³ − x + 4
💡 Key Concept: Classification of polynomials according to degree.
⚠️ Common Mistake: Writing a polynomial whose highest power is different from the required degree.
🎯 Exam Tip: Always check the highest exponent before writing the answer.
Q3. What are the coefficients of x² and x³ in the polynomial x⁴ − 3x³ + 6x² − 2x + 7?
Given:
p(x) = x⁴ − 3x³ + 6x² − 2x + 7
To Find:
The coefficients of x² and x³.
Solution:
In the polynomial
x⁴ − 3x³ + 6x² − 2x + 7
The coefficient of x² is 6.
The coefficient of x³ is −3.
- Coefficient of x² = 6
- Coefficient of x³ = −3
💡 Key Concept: Coefficient is the numerical factor of a term.
⚠️ Common Mistake: Ignoring the negative sign of the coefficient.
🎯 Exam Tip: Always include the sign with the coefficient.
Q4. What is the coefficient of z in the polynomial 4z³ + 5z² − 11?
Given:
4z³ + 5z² − 11
To Find:
The coefficient of z.
Solution:
The polynomial contains the terms:
4z³, 5z² and −11
There is no term containing z.
Therefore, the coefficient of z is 0.
Coefficient of z = 0
💡 Key Concept: Missing terms have coefficient zero.
⚠️ Common Mistake: Taking −11 as the coefficient of z.
🎯 Exam Tip: If a term is absent, its coefficient is always zero.
Q5. What is the constant term of the polynomial 9x³ + 5x² − 8x − 10?
Given:
9x³ + 5x² − 8x − 10
To Find:
The constant term.
Solution:
The constant term is the term without any variable.
In the polynomial
9x³ + 5x² − 8x − 10
The term without x is −10.
Therefore,
Constant term = −10
Constant term = −10
💡 Key Concept: Constant term contains no variable.
⚠️ Common Mistake: Confusing coefficient with constant term.
🎯 Exam Tip: The constant term is always the term without any variable.
📋 Exercise 2.1 Summary
- The degree of a polynomial is the highest power of the variable.
- A constant polynomial has degree 0.
- A linear polynomial has degree 1.
- A quadratic polynomial has degree 2.
- A cubic polynomial has degree 3.
- The coefficient always includes its sign.
- Missing terms have coefficient zero.
- The constant term does not contain any variable.
❓ Frequently Asked Questions
What is a polynomial?
An algebraic expression consisting of variables and constants with non-negative powers.
What is the degree of a polynomial?
The highest power of the variable.
What is a coefficient?
The numerical factor of a variable.
Is this Class 9 Maths Chapter 2 Exercise 2.1 Solutions prepared by experieced teacher?
Absolutely Mr Rakesh sir has 18y+ experience.
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📘 Download Class 9 Maths NCERT Book (Ganita Manjari 2026)
For better understanding of concepts, students should always refer to the original NCERT textbook. You can download the official Class 9 Maths book directly from the NCERT website.
This will help you practice questions exactly as per CBSE exam pattern and improve conceptual clarity.
📥 Download NCERT Class 9 Maths BookSource: Official NCERT Website