**NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.1****NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.2****NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.3****NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.4**

**NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 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}

**Solution:
(i)** 4x

^{2}– 3x + 7

It
is a polynomial in one variable, i.e., x, because each exponent of x is a whole
number.

**(ii)**
y^{2} + √2

It is a polynomial in one variable, i.e., y, because each exponent of y is a
whole number.

**(iii)**
3√t + t√2 = 3(t)^{1/2} + √2.t

It is not a polynomial, because one of the exponents of t is 1/2, which is not a whole number.

**(iv)** y + 2/y = y + 2.y^{-1}

It is not a polynomial, because one of the exponents of y is -1, which is not a
whole number.

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

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

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}

**(iii)**Ï€/2 . x

^{2}+ x

**(iv)**√2 x – 1

**Solution:****
(i)** The given polynomial is 2 + x

^{2}+ x.

The coefficient of x

^{2}is 1.

**(ii)**The given polynomial is 2 – x

^{2}+ x

^{3}.

The coefficient of x

^{2}is -1.

**(iii)**The given polynomial is Ï€/2 . x

^{2}+ x.

The coefficient of x

^{2}is Ï€/2.

**(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.

**Solution:****
(i)** A binomial of degree 35 can be written as 2x

^{35}+ 5.

**(ii)**A monomial of degree 100 can be written as 4y

^{100}– 3.

**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

**Solution:****
(i)** The given polynomial is 5x

^{3}+ 4x

^{2}+ 7x.

The highest power of the variable x is 3.

So, the degree of the polynomial is 3.

**(ii)**The given polynomial is 4 – y

^{2}.

The
highest power of the variable y is 2.

So, the degree of the polynomial is 2.

**(iii)**
The given polynomial is 5t – √7.

The
highest power of the variable t is 1.

So,
the degree of the polynomial is 1.

**(iv)**
The given polynomial is 3.

Since,
3 can be written as 3x^{0}. That is 3 = 3x^{0} [∵ x^{0 }= 1]

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 }

**Solution:****
(i)** The highest degree of x

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

**(ii)**The highest degree of x – x

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

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

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

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

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

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

**Related Links:**

**NCERT Solutions for Maths Class 10**

**NCERT Solutions for Maths Class 11**