**Chapter 2 Polynomials 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+**2y

**(v) x**

^{10}+ y^{3}+t^{50}**Solution:**

**(i)**4x

^{2}– 3x + 7 is an expression having only non-negative integral powers of x. So, it is a polynomial.

**(ii)**y

^{2}+√2 is an expression having only non-negative integral power of y. So, it is a polynomial.

**(iii)**3√t + √2 is an expression in which one term namely 3√t has rational power of f. So, it is not a polynomial.

**(iv)**y+ 2y is an expression in which one term namely 2y ⇒ i.e., 2y

^{-1}has negative power of y. So, it is not a polynomial.

**(v)**x

^{10}+ y

^{3}+ t

^{50}is an expression which has 3 variables.

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

**(i) 2 + x**

(ii) 2 – x2 + x3

^{2}+ x(ii) 2 – x2 + x3

**(iii)**π2

**x**

(iv) √2 x – 1

Solution:

(i)The coefficient of x

^{2}+ x(iv) √2 x – 1

Solution:

(i)

^{2}in 2 + x

^{2}+ x is 1.

**(ii)**The coefficient of x

^{2}in 2 – x

^{2}+ x

^{3}is – 1.

**(iii)**The coefficient of x

^{2}in π2 x

^{2}+ x is π2 .

**(iv)**The coefficient of x

^{2}in

**√**2 x -1 is 0.

**Question 3.Give one example each of a binomial of degree 35, and of a monomial of degree 100.Solution:(i)** y

^{35}+ 2 is a binomial of degree 35.

**(ii)**y

^{100}is a monomial of degree 100.

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

**(i) 5x**

^{3}+4x^{2}+ 7x**(ii) 4 – y**

^{2}(iii) 5f – √7**(iv) 3**

Solution:

(i) In a polynomial 5x

Solution:

^{3}+ 4x

^{2}+ 7x, the highest power of variable x is 3, hence degree of polynomial is 3.

(ii) In a polynomial 4 – y

^{2}, the highest power of variable y = 2, hence degree of polynomial is 2.

(iii) In a polynomial 5t – √7 , the highest power of variable t = 1, hence the degree of polynomial is 1.

(iv) In a polynomial 3, the highest power of variable y = 0, hence the degree of polynomial is 0.

**Question 5.Classify the following as linear, quadratic and cubic polynomials.**

**(i) x**

^{2}+ x**(ii) x – x**

^{3}**(iii) y + y**

^{2}+4**(iv) 1 + x**

**(v) 3t**

**(vi) r**

^{2}**(vii) 7x**

^{3}^{}

**Solution:**

(i) The degree of polynomial x

^{2}+ 2 is 2, hence it is a quadratic polynomial.

(ii) The degree of polynomial x – x

^{3}is 3, hence it is a cubic polynomial.

(iii) The degree of polynomial y + y

^{2}+ 4 is 2, hence it is a quadratic polynomial.

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

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

(vi) The degree of polynomial r

^{2}is 2, hence it is a quadratic polynomial.

(vii) The degree of polynomial 7x

^{3}is 3, hence it is a cubic polynomial.