## 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 *x*, *y*, 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 *x*^{100}.

#### 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.