# Class 9 NCERT Solutions – Chapter 2 Polynomials – 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) 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)The algebraic expression 4x^{2}– 3x + 7 can be written as 4x^{2}– 3x + 7x^{0}As we can see, all exponents of

xare whole numbers,

So, the given expression4x^{2}– 3x + 7is polynomial in one variable.

(ii)The algebraic expression y^{2}+ √2 can be written as y^{2}+ √2y^{0}As we can see, all exponents of

yare whole numbers,

So, the given expressiony^{2}+ √2is polynomial in one variable.

(iii)The algebraic expression 3 √t + t√2 can be written as 3 t^{1/2}+ √2.tAs we can see, one exponent of

tis 1/2, which is not a whole number,

So, thegiven expression3 √t + t√2is not a polynomial in one variable.

(iv)The algebraic expression y + 2/y can be written as y + 2.y^{-1}As we can see, one exponent of

yis -1, which is not a whole number,

So, thegiven expressiony+ 2/yis not a polynomial in one variable.

(v)The given algebraic expression is x^{10}+ y^{3}+ t^{50}As we can see, the expression contains

threevariables i.ex, y, andt,

So, the given expression x^{10 }+ y^{3 }+ t^{50 }is not a polynomial in one variable.

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

^{2}

**(i) 2 + x**^{2}** + x****(ii) 2 – x**^{2}** + x**^{3}**(iii) pi/2 x**^{2}** + x****(iv) √2x – 1**

**Solution: **

(i)The given algebraic expression is 2 + x^{2}+ xAs we can clearly see,

the coefficient of x^{2 }is 1.

(ii)The given algebraic expression is 2 – x^{2}+ x^{3}As we can clearly see,

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

(iii)The given algebraic expression is pi/2 x^{2}+ xAs we can clearly see,

the coefficient of x^{2 }is pi/2.

(iv)The given algebraic expression is √2 x — 1As we can clearly see,

the coefficient of x^{2 }is 0.

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

**Solution: **

A Binomial having degree 35 is

4x^{35}+ 50A Monomial having degree 100 is

3t^{100}pi

**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: **

The highest power of a variable in the given expression is known as the

Degree of the polynomial

(i)The given expression is 5x^{3 }+ 4x^{2}+ 7xAs we can clearly see, the highest power of variable

x is 3,

So, the degree of given polynomial 5x^{3}+4x^{2}+ 7x is 3.

(ii)The given expression is 4 – y^{2}As we can clearly see, the highest power of variable

y is 2,

So, the degree of given polynomial 4 – y^{2}is 2.

(iii)The given expression is 5t – √7As we can clearly see, the highest power of variable

tis 1,

So, the degree of given polynomial 5t – √7 is 1.

(iv)The given expression 3 can be written as 3x^{0}As we can clearly see, the highest power of variable

xis 0,

So, the degree of given polynomial 3 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)Since the degree of given polynomial x^{2 }+ x is 2,

So, it is a Quadratic Polynomial.

(ii)Since the degree of given polynomial x – x^{3}is 3,

So, it is a Cubic Polynomial.

(iii)Since the degree of given polynomial y + y^{2 }+ 4 is 2,

So, it is a Quadratic Polynomial.

(iv)Since the degree of given polynomial 1 + x is 1,

So, it is a Linear Polynomial.

(v)Since the degree of given polynomial 3t is 1,

So, it is a Linear Polynomial.

(vi)Since the degree of given polynomial r^{2}is 2,

So, it is a Quadratic Polynomial.

(vii)Since the degree of given polynomial 7x^{3}is 3,

So, it is a Cubic Polynomial.

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