# NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.1

## Introduction:

In this exercise/article we will learn about Polynomials. We know variable but i explain variable is x , y , z \(\displaystyle \infty \), coefficient and zero polynomial. The degree of a non - zero constant polynomial is zero. In particular , if \(\displaystyle {{a}_{0}}\,=\,{{a}_{1}}\,=\,{{a}_{2}}\,=\,{{a}_{3}}\,=\,.....\,=\,{{a}_{n}}\,=\,0\) ( all the constants are zero ), we get the zer0 polynomial, which is denoted by 0.

- ( x + y )
^{2}= x^{2}+ 2xy + y^{2} - ( x - y )
^{2}= x^{2}- 2xy + y^{2} - x
^{2}- y^{2}= ( x + y ) ( x - y )

In addition to the above, we shall study some more algebraic identity and their use in factorisation and in evaluating some given expressions.

NCERT Class 9 Maths Chapter 2 Polynomials :

- NCERT Class 9 Maths Chapter 2 Polynomials Exercise 2.1
- NCERT Class 9 Maths Chapter 2 Polynomials Exercise 2.2
- NCERT Class 9 Maths Chapter 2 Polynomials Exercise 2.3
- NCERT Class 9 Maths Chapter 2 Polynomials Exercise 2.4
- NCERT Class 9 Maths Chapter 2 Polynomials Exercise 2.5
- Extra Questions Class 9 Maths Chapter 2 Polynomials

**Class 9 Maths Exercise 2.1 (Page-32)**

**Q1. **Which of the following expressions are polynomials in one variable and Which are not? State reasons for your answer.

**(i) **4x^{2} - 3x + 7

**Solution :**

We have 4x^{2} - 3x + 7

In the above case Polynomial only one variable = x

**(ii) **y^{2} + √2

**Solution :**

We have ** **y^{2} + √2

In the above case Polynomial only one variable = y

**(iii)** 3√t + t√2

**Solution :**

We have 3√t + t√2

In the above case in one variable but ( t ) of power is not whole number.

**(iv)** y + \(\displaystyle \frac{2}{y}\)

**Solution :**

We have y + \(\displaystyle \frac{2}{y}\)

In the above case in one variable but ( \(\displaystyle {{y}^{{-1}}}\) ) of power is not whole number.

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

**Solution :**

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

In the above case Polynomial is three variable = x , y and t

**Q2.** Write the coefficients of x^{2} in each of the following :

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

**Solution :**

We have 2 + x^{2} + x

The coefficient of x^{2} = 1

**(ii) **2 - x^{2} + x^{3}

**Solution :**

We have 2 - x^{2} + x^{3}

The coefficient x^{2} = -1

**(iii) **\(\displaystyle \frac{\pi }{2}{{x}^{2}}\,+\,x\)

**Solution :**

We have \(\displaystyle \frac{\pi }{2}{{x}^{2}}\,+\,x\)

The coefficient of x^{2} = \(\displaystyle \frac{\pi }{2}\)

**(iv) **√2x - 1

**Solution :**

We have ** **√2x - 1

The coefficient of x^{2} = 0

**Q3. **Give one example each of a binomials of degree 35, and of a monomials of degree 100.

**Solution :**

A binomial of degree 35 = 3x^{35} + 4

A monomials of degree 100 = 3x^{100} - 4

# NCERT Solutions Class 9 Maths

**Q4. **Write the degree of each of the following polynomials :

**(i) **5x^{3} + 4x^{2} + 7x

**Solution :**

We have 5x^{3} + 4x^{2} + 7x

The highest degree of the variable = 3

**(ii) **4 - y^{2}

**Solution :**

We have 4 - y^{2}

The highest degree of the variable = 2

**(iii) **5t - √7

**Solution :**

We have ** **5t - √7

The highest degree of the variable = 1

**(iv) **3

**Solution :**

We have 3

The highest degree of the variable = 0

**Q5. **Classify the following as linear , quadratic and cubic polynomials :

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

**Solution :**

We have ** **x^{2} + x

The degree of ** **x^{2} + x = 2

So, it is a Quadratic polynomial

**(ii) **x - x^{3}

**Solution :**

We have x - x^{3}

The degree of x - x^{3} = 3

So, it is a cubic polynomial

**(iii) **y + y^{2} + 4

**Solution :**

We have y + y^{2} + 4

The degree of y + y^{2} + 4 = 2

So, it is a quadratic polynomial

**(iv) **1 + x

**Solution :**

We have 1 + x

The degree of 1 + x = 1

So, it is a linear polynomial

**(v) **3t

**Solution :**

We have 3t

The degree of 3t = 1

So, it is a linear polynomial

**(vi) **r^{2}

**Solution :**

We have r^{2}

The degree of r^{2} = 2

So, it is a quadratic polynomial

**(vii) **7x^{3}

**Solution :**

We have 7x^{3}

The degree of 7x^{3} = 3

So, it is a cubic polynomial.