**Download NCERT Solutions For Class 9 Maths Chapter 2 Exercise 2.1 – Polynomials**

**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 +

(iii) 3√t + t√2

(iv) y +

**(v) x**

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

(i) 4x^{2} – 3x + 7 : Exponent of each variable in the expression is a whole number and has one variable i.e. x . Therefore it is polynomial in one variable.

(ii) y^{2} + √2 : Exponent of each variable in the expression is a whole number and has one variable i.e. y . Therefore it is polynomial in one variable.

(iii) 3√t + t√2 : Exponent of t in the term √t is i.e. not a whole number . Therefore it is not a polynomial.

(iv) y + : Exponent of y in the term is -1 i.e. not a whole number . Therefore it is not a polynomial.

(v) x^{10} + y^{3} + t^{50} : There is more than one variable in the expression . Therefore it is not a polynomial in one variable.

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

**(i) 2 + x ^{2} + x
(ii) 2 – x^{2} + x^{3}
(iii) **

**+ x**

**(iv) √2**

**x − 1**

** ****Solution : **

(i) 2 + x^{2} + x : Coefficients of x^{2} = 1

(ii) 2 – x^{2} + x^{3} : Coefficients of x^{2} = -1

(iii) + x : Coefficients of x^{2} =

(iv) √2x − 1

The given expression can be written as

0x^{2} + √2x − 1 : Coefficients of x^{2} = 0.

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

**Solution :**

A binomial of degree 35 must contain two terms where the highest exponent of the variable should be 35.

For example = **x ^{35 }+ 5**

A monomial of degree 100 must contain one term where the exponent of the variable should be 100.

For example** = ****x ^{100} **

**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

(iv) 3

**Solution :**

The degree of a polynomial is defined as the highest power of the variable in the polynomial. Therefore we can find the degree of the given polynomials as :

(i) 5x^{3} + 4x^{2} + 7x : Degree = 3

(ii) 4 – y^{2} : Degree = 2

(iii) 5t – √7 : Degree = 1

(iv) 3 = 3x^{0} : Degree = 0

**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

(vii) 7x

(vi) r

^{2}(vii) 7x

^{3}

**Solution:**

If the degree of a polynomial is one , it is called a linear polynomial and if the degree is two and three then it is called quadratic and cubic polynomial respectively.

(i) x^{2} + x : Degree = 2 , Quadratic.

(ii) x – x^{3} : Degree = 3 , Cubic.

(iii) y + y^{2} + 4 : Degree = 2 , Quadratic.

(iv) 1 + x : Degree = 1 , Linear.

(v) 3t : Degree = 1 , Linear.

(vi) r^{2} : Degree = 2 , Quadratic.

(vii) 7x^{3} : Degree = 3 , Cubic.

**Download NCERT Solutions For Class 9 Maths Chapter 2 Exercise 2.1 – Polynomials**

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