NCERT Solutions Class 9 Mathematics Polynomials Exercise 2.1

Exercise 2.1

Question :

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

Answer :

(i) 4x² – 3x + 7

There is only one variable x with whole number power. So, this polynomial is in one variable.      

(ii) y² + √2        

There is only one variable y with whole number power. So, this polynomial is in one variable.

(iii) 3√t + t√2

There is only one variable t but in 3√t, power of t is 1/2 which is not a whole number. So this is

not a polynomial.           

(iv) y + 2/y            

There is only one variable y but in 2/y, power of y is -1/2 which is not a whole number. So this

is not a polynomial.

(v) x¹⁰ + y³ + t⁵⁰

There are three variables x, y and z and these powers are whole number. So this is not a

polynomial.

Question : 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

Answer :

(i) 2 + x² + x = 2 + 1 * x² + x               

So, the coefficient of x² is 1

(ii) 2 – x² + x³ = 2 + (-1)x² + x³            

So, the coefficient of x² is -1

(iii) π/2 * x² + x               

So, the coefficient of x² is π/2

(iv) √2x – 1 = √2x + 0 * x² – 1

 So, the coefficient of x² is 0

Question : 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Answer :

A binomial of degree 35 = x³⁵ + 7

A binomial of degree 100 = 2x¹⁰⁰

Question : 4: Write the degree of each of the following polynomials:

(i) 5x³ + 4x² + 7x                 (ii) 4 – y²                (iii) 5t – √7               (iv) 3

Answer :

(i) The degree of 5x³ + 4x² + 7x is 3                 

(ii) The degree of 4 – y² is 2              

(iii) The degree of 5t – √7 = 5t¹ – √7 is 1               

(iv) The degree of 3 = 3x⁰ is 0