## Polynomials

## Chapter 2

## Exercise 2.1

**EX 2.1 QUESTION 1.**

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

**(i) 4x ^{2}–3x+7**

**(ii) y ^{2}+√2**

**(iii) 3√t+t√2**

**(iv) y+2/y**

**(v) x ^{10}+y^{3}+t^{50}**

**Solution:**

(i) 4x^{2}–3x+7

The given equation has x is the only variable. So, the polynomial in one variable.

(ii) y^{2}+√2

The given equation has y is the only variable. So, the polynomial in one variable.

(iii) 3√t+t√2

= 3 √t^{1/2} + √2.t

It is in one variable but not polynomial because it contains (t^{1/2}) which is not a whole number.

(iv) y+2/y

= y + 2.y^{-1}

It is in one variable but not polynomial because it contains (y^{-1}) which is not a whole number.

(v) x^{10}+y^{3}+t^{50}

It is a polynomial in three variables x, y and t. So, it is not a polynomial in one variable.

**EX 2.1 QUESTION 2.**

** Write the coefficients of x ^{2} in each of the following:**

**(i) 2+x ^{2}+x**

**(ii) 2–x ^{2}+x^{3}**

**(iii) (π/2)x ^{2}+x**

**(iii)√2x-1**

**Solution:**

(i) 2 + x^{2} + x.

The coefficient of x^{2} is 1.

(ii) 2 – x^{2} + x^{3}.

The coefficient of x^{2} is -1.

(iii) ** **+ x.

The coefficient of x^{2} is **.**

(iv) √2 x – 1.

The coefficient of x^{2} is 0.

**EX 2.1 QUESTION 3.**

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

**Solution:**

(i) A binomial of degree 35 = 3x^{35} -4.

(ii) A monomial of degree 100 = 3x^{100}.

**EX 2.1 QUESTION 4.**

**Write the degree of each of the following polynomials.**

**(i) 5x ^{3}+4x^{2} + 7x**

**(ii) 4 – y**

^{2}**(iii) 5t – √7**

**(iv) 3**

**Solution:**

(i) The degree of 5x^{3} + 4x^{2} + 7x = 3.

(ii) The degree of 4- y^{2 = } 2.

(iii) The degree of 5t – √7 = 5t^{1} – √7 = 1

(iv) The degree of 3 = 3x° = 0 [∵ x°=1]