**NCERT Solutions for Class 9 Maths Chapter-2 Polynomials Exercise 2.1**

**Ex 2.1 Class 9 Maths 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}

Sol. (i) We can write the equation 4x^{2} – 3x + 7 as

= 4x^{2} – 3x + 7x^{0}

Since, x is the only variable in this equation,

It is a polynomial in one variable i.e., x

because each exponent of x is a whole number.

(ii) We have y^{2} + √2 = y^{2} + √2y^{0}

Since, y is the only variable in this equation,

It is a polynomial in one variable i.e., y

because each exponent of y is a whole number.

(iii) We have 3√t + t√2 = 3t^{1/2} + √2t

because t is the only variable in this equation,

It is not a polynomial, because one of the exponents of t is 1/2,

which is not a whole number.

(iv) We have y+2y=y+2y-1

As we can see, y is the only variable in this equation,

It is not a polynomial, because one of the exponents of y is -1,

which is not a whole number.

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

Here, the exponent of every variable is a whole number, but x^{10}+ y^{3} + t^{50} is a polynomial in x, y and t, i.e., in three variables.

So, it is not a polynomial in one variable.

**Ex 2.1 Class 9 Maths Question 2.**

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

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

**(ii) 2 – x ^{2} + x^{3}**

**(iv) √2 x – 1**

Sol. (i) The given polynomial is 2 + x^{2} + x

It can be written as, 2 + (1)x^{2} + x

The coefficient of x^{2} is 1.

(ii) The given polynomial is 2 – x^{2} + x^{3}

It can be written as, 2 – (1)x^{2} + x^{3}

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

(iv) The given polynomial is √2 x – 1

It can be written as (0)x^{2}+√2 x – 1

The coefficient of x^{2} is 0

**Ex 2.1 Class 9 Maths Question 3.**

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

Sol. (i) A binomial of degree 35 can be 7x^{35} -2.

(ii) A monomial of degree 100 can be 3y^{100}.

**Ex 2.1 Class 9 Maths 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**

Sol.

(i) It is given that, 5x^{3} + 4x^{2} + 7x.

The highest power of the variable x is 3.

So, the degree of the polynomial is 3.

(ii) In polynomial 4 – y^{2}.

The highest power of the variable y is 2.

So, the degree of the polynomial is 2.

(iii) In the given polynomial 5t – √7.

The highest power of variable t is 1.

So, the degree of the polynomial is 1.

(iv) As we know, 3 = 3x°

So, the degree of the polynomial is 0.

**Ex 2.1 Class 9 Maths 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}

Sol. Linear polynomial: A polynomial of degree one.

Quadratic Polynomial: A polynomial of degree two.

Cubic Polynomial: A polynomial of degree three.

(i) The degree of x^{2} + x is 2. So, it is a quadratic polynomial.

(ii) The degree of x – x^{3} is 3. So, it is a cubic polynomial.

(iii) The degree of y + y^{2} + 4 is 2. So, it is a quadratic polynomial.

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

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

(vi) The degree of r^{2} is 2. So, it is a quadratic polynomial.

(vii) The degree of 7x^{3} is 3. So, it is a cubic polynomial.