NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

## 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) We have 4x^{2} – 3x + 7 = 4x^{2} – 3x + 7x^{0}

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}

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 = 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) We have y + 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) We have 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 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}

(iii) π/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 π/2x2 + x.

The coefficient of x^{2} is π/2.

(iv) The given polynomial is √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) Abmomial of degree 35 can be 3x^{35} -4.

(ii) A monomial of degree 100 can be √2y^{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

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 variable t is 1. So, the degree of the polynomial is 1.

(iv) Since, 3 = 3x° [∵ x°=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 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.

### NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.2

### NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3

### NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.4

### NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.5

**Ex 2.5 Class 9 Maths Question 1**

**Ex 2.5 Class 9 Maths Question 2**

**Ex 2.5 Class 9 Maths Question 3**

**Ex 2.5 Class 9 Maths Question 4**

**Ex 2.5 Class 9 Maths Question 5**

**Ex 2.5 Class 9 Maths Question 6**

**Ex 2.5 Class 9 Maths Question 7**

**Ex 2.5 Class 9 Maths Question 8**

**Ex 2.5 Class 9 Maths Question 9**

**Ex 2.5 Class 9 Maths Question 10**

**Ex 2.5 Class 9 Maths Question 11**

**Ex 2.5 Class 9 Maths Question 12**

**Ex 2.5 Class 9 Maths Question 13**

**Ex 2.5 Class 9 Maths Question 14**

**Ex 2.5 Class 9 Maths Question 15**

**Ex 2.5 Class 9 Maths Question 16**

## Polynomials Class 9 Extra Questions Maths Chapter 2

**Extra Questions for Class 9 Maths Chapter 2 Polynomials**