NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.1
Class 9 Maths Chapter 2 - Polynomials Exercise 2.1 gives you a basic idea of polynomials. In this exercise, you will learn how to check whether a given expression is a polynomial, and how to find out the degree, terms, and coefficients of the polynomial. It is very important to understand the terms given in this exercise as they are the base for all other topics related to this chapter.
Understanding Exercise 2.1 will definitely help you answer problems easily in your exams, particularly questions related to expressions in algebra identities. All the questions in this exercise follow the latest NCERT syllabus to ensure you are practicing the right kind of problems for your CBSE exams.
To help you build better understanding, NCERT Solutions for Exercise 2.1 are accurate and simple. Use the PDF to improve on understanding clearly and getting better marks in maths.
1.0Download NCERT Solutions of Class 9 Maths Chapter 2 Polynomials Exercise 2.1: Free PDF
This exercise of NCERT Solutions for Class 9 Maths Chapter 2 will help you in the understanding of what polynomials are, and how to find their terms, degree and coefficients.. Download the free PDF of the NCERT Solutions from below.
2.0NCERT Exercise Solutions Class 9 Chapter 2- Polynomials: All Exercises
3.0NCERT Class 9 Maths Chapter 2 Exercise 2.1 : Detailed Solutions
1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x²−3x+7
(ii) y²+√2
(iii) 3√t+t√2
(iv) y+2/y
(v) x¹⁰+y³+t⁵⁰
Sol. (i) 4x²−3x+7
This expression is a polynomial in one variable x because there is only one variable (x) in the expression, and all exponents of x are whole numbers.
(ii) y²+√2
This expression is a polynomial in one variable y because there is only one variable (y) in the expression, and all exponents of y are whole numbers.
(iii) 3√t+t√2
The expression is not a polynomial because in the term 3√t (which is 3t¹ᐟ²), the exponent of t is 1/2, which is not a whole number.
(iv) y+2/y = y+2y⁻¹
The expression is not a polynomial because the exponent of y is (−1) in the term 2/y (which is 2y⁻¹), and -1 is not a whole number.
(v) x¹⁰+y³+t⁵⁰
The expression is not a polynomial in one variable; it is a polynomial in 3 variables x, y and t.
2. Write the coefficients of x² in each of the following :
(i) 2+x²+x
(ii) 2−x²+x³
(iii) (π/2)x²+x
(iv) √2x−1
Sol. (i) 2+x²+x
Coefficient of x² = 1
(ii) 2−x²+x³
Coefficient of x² = −1
(iii) (π/2)x²+x
Coefficient of x² = π/2
(iv) √2x−1
This expression can be written as 0x² + √2x − 1.
Coefficient of x² = 0
3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Sol. One example of a binomial of degree 35 is 3x³⁵−4. (A binomial has two terms, and its degree is the highest exponent).
One example of monomial of degree 100 is 5x¹⁰⁰. (A monomial has one term, and its degree is the exponent of the variable).
4. Write the degree of each of the following polynomials :
(i) 5x³+4x²+7x
(ii) 4−y²
(iii) 5t−√7
(iv) 3
Sol. (i) 5x³+4x²+7x
The term with the highest power of x = 5x³.
The exponent of x in this term = 3. Therefore, the degree of this polynomial = 3.
(ii) 4−y²
The term with the highest power of y = −y².
The exponent of y in this term = 2. Therefore, the degree of this polynomial = 2.
(iii) 5t−√7
The term with highest power of t = 5t.
The exponent of t in this term = 1. Therefore, the degree of this polynomial = 1.
(iv) 3
This is a constant polynomial (can be written as 3x⁰) which is non-zero. Therefore, the degree of this polynomial = 0.
5. Classify the following as linear, quadratic and cubic polynomials :
(i) x²+x
(ii) x−x³
(iii) y+y²+4
(iv) 1+x
(v) 3t
(vi) r²
(vii) 7x³
Sol.
(i) x²+x: Highest power is 2, so it's Quadratic.
(ii) x−x³: Highest power is 3, so it's Cubic.
(iii) y+y²+4: Highest power is 2, so it's Quadratic.
(iv) 1+x: Highest power is 1, so it's Linear.
(v) 3t: Highest power is 1, so it's Linear.
(vi) r²: Highest power is 2, so it's Quadratic.
(vii) 7x³: Highest power is 3, so it's Cubic.
4.0Key Features and Benefits Class 9 Maths Chapter 2 Number System: Exercise 2.1
- NCERT Solutions of Exercise 2.1 introduces you to polynomials, their terms, coefficients, and degrees.
- All questions here are based on the latest NCERT syllabus.
- The exercise helps build a strong foundation that is useful for higher classes.
- Regularly practicing NCERT Solutions helps you solve polynomial questions quickly and without confusion.
- Solutions are provided in a step by step format to improve your understanding and help in quick revision
- Regular practice boosts confidence for CBSE exams and sharpens skills for competitive exams like the olympiads.