Class 9 Maths Chapter 2 Polynomials – Exercise 2.1 NCERT Solutions

Introduction

Exercise 2.1 introduces polynomials. You’ll learn how to identify polynomials, classify them based on degree, and distinguish between monomials, binomials, and trinomials.

Key Formula Used

• Polynomial Definition: An algebraic expression of the form

$$a_n{x}^n+a_{n-1}{x}^{n-1}+\cdots +a_{1}x+a_0$$

where coefficients $a_i$ are real numbers and $n$ is a non‑negative integer.

• Degree of Polynomial: The highest power of the variable.

Solved Questions (Step by Step)

Q1. Which of the following are polynomials: $x^2+x+1$, $\frac{1}{x}+2$, $\sqrt{x}+3$?

Solution:

• $x^2+x+1$: Yes, polynomial (degree 2).

• $\frac{1}{x}+2$: Not a polynomial (negative power).

• $\sqrt{x}+3$: Not a polynomial (fractional power).

Q2. Classify $x^3+2x^2+5$.

Solution:

• Highest power = 3.

• Degree = 3.

• Polynomial is a cubic trinomial.

Q3. Classify $7x^4$.

Solution:

• Degree = 4.

• Single term → monomial.

• Polynomial is a quartic monomial.

Q4. Classify $2x^2+3x$.

Solution:

• Degree = 2.

• Two terms → binomial.

• Polynomial is a quadratic binomial.

Q5. Classify $5x+7$.

Solution:

• Degree = 1.

• Two terms → binomial.

• Polynomial is a linear binomial.

Q6. Find degree of $x^5+2x^3+7$.

Solution:

• Highest power = 5.

• Degree = 5.

Q7. Find degree of $4x^7+3x^2+1$.

Solution:

• Highest power = 7.

• Degree = 7.

Q8. Find degree of constant polynomial 9.

Solution:

• Constant = degree 0.

Q9. Find degree of zero polynomial.

Solution:

• Zero polynomial has undefined degree.

Q10. Identify type of polynomial: $x^2+2x+1$.

Solution:

• Degree = 2.

• Three terms → trinomial.

• Quadratic trinomial.

Q11. Identify type of polynomial: $x^3-4x$.

Solution:

• Degree = 3.

• Two terms → binomial.

• Cubic binomial.

Q12. Identify type of polynomial: $7x^2$.

Solution:

• Degree = 2.

• One term → monomial.

• Quadratic monomial.

Q13. Identify type of polynomial: $x^4+2x^3+3x^2+4x+5$.

Solution:

• Degree = 4.

• Five terms.

• Quartic polynomial.

Q14. Identify type of polynomial: $2x^5+3x^2$.

Solution:

• Degree = 5.

• Two terms → binomial.

• Quintic binomial.

Q15. Identify type of polynomial: $x^6$.

Solution:

• Degree = 6.

• One term → monomial.

• Sextic monomial.

Conclusion

Exercise 2.1 has 15 questions that help you understand the basics of polynomials, their classification, and degrees. This foundation is essential for solving higher‑order polynomial problems in later exercises.

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