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 = x² + 2xy + y²
• ( x - y )² = x² - 2xy + y²
• x² - y² = ( 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) 4x² - 3x + 7

Solution :

We have 4x² - 3x + 7

In the above case Polynomial only one variable = x

(ii) y² + √2

Solution :

We have  y² + √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) x¹⁰ + y³ + t⁵⁰

Solution :

We have x¹⁰ + y³ + t⁵⁰

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

Q2. Write the coefficients of x² in each of the following :

(i) 2 + x² + x

Solution :

We have 2 + x² + x

The coefficient of x² = 1

(ii) 2 - x² + x³

Solution :

We have 2 - x² + x³

The coefficient x² = -1

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

Solution :

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

The coefficient of x² = \(\displaystyle \frac{\pi }{2}\)

(iv) √2x - 1

Solution :

We have  √2x - 1

The coefficient of x² = 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 = 3x³⁵ + 4

A monomials of degree 100 = 3x¹⁰⁰ - 4

 

NCERT Solutions Class 9 Maths

 

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

(i) 5x³ + 4x² + 7x

Solution :

We have 5x³ + 4x² + 7x

The highest degree of the variable = 3

(ii) 4 - y²

Solution :

We have 4 - y²

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) x² + x

Solution :

We have  x² + x

The degree of  x² + x = 2

So, it is a Quadratic polynomial

(ii) x - x³

Solution :

We have x - x³

The degree of x - x³ = 3

So, it is a cubic polynomial

(iii) y + y² + 4

Solution :

We have y + y² + 4

The degree of y + y² + 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) r²

Solution :

We have r²

The degree of r² = 2

So, it is a quadratic polynomial

(vii) 7x³

Solution :

We have 7x³

The degree of 7x³ = 3

So, it is a cubic polynomial.

 

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