Download NCERT Solutions For Class 9 Maths Chapter 2 Exercise 2.1 – Polynomials contains 5 questions, for which detailed answers have been provided in this note.
| Category | NCERT Solutions for Class 9 |
| Subject | Maths |
| Chapter | Chapter 2 |
| Exercise | Exercise 2.1 |
| Chapter Name | Polynomials |
Download NCERT Solutions For Class 9 Maths Chapter 2 Exercise 2.1 – Polynomials
NCERT Solutions For Class 9 Maths Chapter 2 Exercise 2.1 – Polynomials
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
 Solution:
(i) 4x2 – 3x + 7 : Exponent of each variable in the expression is a whole number and has one variable i.e. x . Therefore it is polynomial in one variable.
(ii) y2 + √2 : Exponent of each variable in the expression is a whole number and has one variable i.e. y . Therefore it is polynomial in one variable.
(iii) 3√t + t√2 : Exponent of t in the term √t is 1/2 i.e. not a whole number . Therefore it is not a polynomial.
(iv) y + 2/y : Exponent of y in the term 2/y is -1 i.e. not a whole number . Therefore it is not a polynomial.
(v) x10 + y3 + t50 : There is more than one variable in the expression . Therefore it is not a polynomial in one variable.
2. Write the coefficients of x2 in each of the following:
(i) 2 + x2 + x
(ii) 2 – x2 + x3
(iii) (Î /2)x2 Â + x
(iv) √2x − 1
 Solution :
(i) 2 + x2 + x :   Coefficients of x2  = 1
(ii) 2 – x2 + x3 :   Coefficients of x2  = -1
(iii) (Î /2)x2 + x : Coefficients of x2 = (Î /2)
(iv) √2x − 1
The given expression can be written as
0x2 + √2x − 1 : Coefficients of x2  = 0.
3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution :
A binomial of degree 35 must contain two terms where the highest exponent of the variable should be 35.
For example =Â x35 + 5
A monomial of degree 100 must contain one term where the exponent of the variable should be 100.
For example = x100Â
4. Write the degree of each of the following polynomials:
(i) 5x3 + 4x2 + 7x
(ii) 4 – y2
(iii) 5t – √7Â
(iv) 3
Solution :
The degree of a polynomial is defined as the highest power of the variable in the polynomial. Therefore we can find the degree of the given polynomials as :
(i) 5x3 + 4x2 + 7x : Degree =Â 3
(ii) 4 – y2 : Degree =Â 2
(iii) 5t – √7 : Degree = 1
(iv) 3 = 3x0 : Degree =Â 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) 7x3Â
Solution:
If the degree of a polynomial is one , it is called a linear polynomial and if the degree is two and three then it is called quadratic and cubic polynomial respectively.
(i) x2 + x : Degree =Â 2 , Quadratic.
(ii) x – x3 : Degree =Â 3 , Cubic.
(iii) y + y2 + 4 : Degree =Â 2 , Quadratic.
(iv) 1 + x : Degree =Â 1 , Linear.
(v) 3t : Degree =Â 1 , Linear.
(vi) r2 : Degree =Â 2 , Quadratic.
(vii) 7x3 : Degree =Â 3 , Cubic.
NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1 – Polynomials, has been designed by the NCERT to test the knowledge of the student on the topic – Polynomials in One Variable
The next Exercise for NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.2 – Number System can be accessed by clicking here.