Polynomial_Soln_2.1

 

NCERT Solutions for Class 9 Maths Exercise 2.1

Question 1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i)

(ii)

(iii)

(iv)

(v)

Solution:

(i)

We can observe that in the polynomial , we have x as the only variable and the powers of x in each term are a whole number.

Therefore, we conclude that is a polynomial in one variable.

(ii)

We can observe that in the polynomial , we have y as the only variable and the powers of y in each term are a whole number.

Therefore, we conclude that is a polynomial in one variable.

(iii)

We can observe that in the polynomial, we have t as the only variable and the powers of t in each term are not a whole number.

Therefore, we conclude thatis not a polynomial in one variable.

(iv)

We can observe that in the polynomial, we have y as the only variable and the powers of y in each term are not a whole number.

Therefore, we conclude thatis not a polynomial in one variable.

(v)

We can observe that in the polynomial, we have x, y and t as the variables and the powers of x, y and t in each term is a whole number.

Therefore, we conclude that is a polynomial but not a polynomial in one variable.

Question 2. Write the coefficients of in each of the following :

(i)

(ii)

(iii)

(iv)

Solution:

(i)

The coefficient ofin the polynomialis 1.

(ii)

The coefficient ofin the polynomialis.

(iii)

The coefficient ofin the polynomialis.

(iv)

The coefficient ofin the polynomial is 0.

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

Solution:

The binomial of degree 35 can be.

The binomial of degree 100 can be.

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

(i)

(ii)

(iii)

(iv)3

Solution:

(i)

We know that the degree of a polynomial is the highest power of the variable in the polynomial.

We can observe that in the polynomial, the highest power of the variable x is 3.

Therefore, we conclude that the degree of the polynomialis 3.

(ii)

We know that the degree of a polynomial is the highest power of the variable in the polynomial.

We can observe that in the polynomial, the highest power of the variable y is 2.

Therefore, we conclude that the degree of the polynomialis 2.

(iii)

We know that the degree of a polynomial is the highest power of the variable in the polynomial.

We observe that in the polynomial, the highest power of the variable t is 1.

Therefore, we conclude that the degree of the polynomialis 1.

(iv)3

We know that the degree of a polynomial is the highest power of the variable in the polynomial.

We can observe that in the polynomial 3, the highest power of the assumed variable x is 0.

Therefore, we conclude that the degree of the polynomial 3 is 0.

Question 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

Solution :

(i) The degree of x2 + x is 2. So, it is a quadratic polynomial.

(ii) The degree of x – x3 is 3. So, it is a cubic polynomial.

(iii) The degree of y + y2 + 4 is 2. So, it is a quadratic polynomial.

(iv) The degree of 1 + x is 1. So, it is a linear polynomial.

(v) The degree of 3t is 1. So, it is a linear polynomial.

(vi) The degree of r2 is 2. So, it is a quadratic polynomial.

(vii) The degree of 7x3 is 3. So, it is a cubic polynomial.