NCERT solution class 9 chapter 2 Polynomials exercise 2.2 mathematics

EXERCISE 2.2


Page No 32:

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) 

Answer:

(i) 

Yes, this expression is a polynomial in one variable x.

(ii) 

Yes, this expression is a polynomial in one variable y.

(iii) 

No. It can be observed that the exponent of variable t in term  is , which is not a whole number. Therefore, this expression is not a polynomial.

(iv) 

No. It can be observed that the exponent of variable y in termis −1, which is not a whole number. Therefore, this expression is not a polynomial.

(v) 

No. It can be observed that this expression is a polynomial in 3 variables xy, and t. Therefore, it is not a polynomial in one variable.


Question 2:

Write the coefficients of in each of the following:

(i)  (ii) 

(iii)  (iv) 

Answer:

(i) 

In the above expression, the coefficient of is 1.

(ii) 

In the above expression, the coefficient of is −1.

(iii) 

In the above expression, the coefficient of  is.

(iv) 

In the above expression, the coefficient of  is 0.


Question 3:

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

Answer:

Degree of a polynomial is the highest power of the variable in the polynomial.

Binomial has two terms in it. Therefore, binomial of degree 35 can be written as .

Monomial has only one term in it. Therefore, monomial of degree 100 can be written as x100.


Question 4:

Write the degree of each of the following polynomials:

(i)  (ii) 

(iii)  (iv) 3

Answer:

Degree of a polynomial is the highest power of the variable in the polynomial.

(i) 

This is a polynomial in variable x and the highest power of variable x is 3. Therefore, the degree of this polynomial is 3.

(ii) 

This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2.

(iii) 

This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1.

(iv) 3

This is a constant polynomial. Degree of a constant polynomial is always 0.


Question 5:

Classify the following as linear, quadratic and cubic polynomial:

(i) (ii)  (iii)  (iv)  (v) 

(vi)  (vii) 

Answer:

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively.

(i)  is a quadratic polynomial as its degree is 2.

(ii) is a cubic polynomial as its degree is 3.

(iii)  is a quadratic polynomial as its degree is 2.

(iv) 1 + x is a linear polynomial as its degree is 1.

(v)  is a linear polynomial as its degree is 1.

(vi) is a quadratic polynomial as its degree is 2.

(vii) is a cubic polynomial as its degree is 3.


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