NCERT Solutions for Exercise 2.1 Class 9 Maths Chapter 2

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

Edited By Safeer PP | Updated on Jul 22, 2022 05:25 PM IST

NCERT Solutions for exercise 2.1 Class 9 Maths chapter 2 polynomials, which would be quite handy when performing assignments. We know that "Polynomial" derives from the words "Poly" (Meaning Many) and "nominal" (in this case meaning Term)—so it means "many terms" as we learned in previous sessions. Exercise 2.1 Class 9 Maths is a chapter-opening exercise that incorporates a number of questions. Here We'll look at polynomials in NCERT book exercise 2.2. The notion of the relationship between polynomials and non-polynomials is explored in chapter 2 of NCERT Mathematics for Class 9.

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Polynomials Class 9 Chapter 2 Exercise: 2.1
More About NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1
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The Class 9 Maths chapter 2 exercise 2.1 lists a few practice problems on polynomials that involve the identification of the degree of Polynomials. The Class 9 Maths chapter 2 exercise 2.1 covers the topics like tracing the coefficients of given polynomials. The concept of classification of polynomials with linear, quadratic, and cubic degrees will also discuss in NCERT syllabus Class 9 Maths chapter 2 exercise 2.1. Along with Class 9 Maths chapter 1 exercise 2.1 the following exercises are also present.

Polynomials Class 9 Chapter 2 Exercise: 2.1

Q1 (i) Is the following expression polynomial in one variable? State reasons for your answer. $4x^2 - 3x + 7$

Answer:

YES
Given polynomial $4x^2 - 3x + 7$ has only one variable which is x

Q1 (ii) Is the following expression polynomial in one variable? State reasons for your answer. $y^2 + \sqrt2$

Answer:

YES
Given polynomial has only one variable which is y

Q1 (iii) Is the following expression polynomial in one variable? State reasons for your answer. $3\sqrt t + t\sqrt2$

Answer:

NO
Because we can observe that the exponent of variable t in term $3\sqrt t$ is $\frac{1}{2}$ which is not a whole number.
Therefore this expression is not a polynomial.

Q1 (iv) Is the following expression polynomial in one variable? State reasons for your answer. $y + \frac{2}{y}$

Answer:

NO
Because we can observe that the exponent of variable y in term $\frac{2}{y}$ is $-1$ which is not a whole number. Therefore this expression is not a polynomial.

Q1 (v) Is the following expression polynomial in one variable? State reasons for your answer. $x^{10} + y^3 + t^{50}$

Answer:

NO
Because in the given polynomial $x^{10} + y^3 + t^{50}$ there are 3 variables which are x, y, t. That's why this is polynomial in three variable not in one variable.

Q2 (i) Write the coefficients of $x^2$ in the following: $2 + x^2 +x$

Answer:

Coefficient of $x^2$ in polynomial $2 + x^2 +x$ is 1.

Q2 (ii) Write the coefficients of $x^2$ in the following: $2 - x^2 + x^3$

Answer:

Coefficient of $x^2$ in polynomial $2 - x^2 + x^3$ is -1.

Q2 (iii) Write the coefficients of $x^2$ in the following: $\frac{\pi}{2}x^2 + x$

Answer:

Coefficient of $x^2$ in polynomial $\frac{\pi}{2}x^2 + x$ is $\frac{\pi}{2}$

Q2 (iv) Write the coefficients of $x^2$ in the following: $\sqrt2 x - 1$

Answer:

Coefficient of $x^2$ in polynomial $\sqrt2 x - 1$ is 0

Q3 Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Answer:

Degree of a polynomial is the highest power of the variable in the polynomial.
In binomial, there are two terms
Therefore, binomial of degree 35 is
Eg:- $x^{35}+1$
In monomial, there is only one term in it.
Therefore, monomial of degree 100 can be written as $y^{100}$

Q4 (i) Write the degree the following polynomial: $5x^3 + 4x^2 + 7x$

Answer:

Degree of a polynomial is the highest power of the variable in the polynomial.
Therefore, the degree of polynomial $5x^3 + 4x^2 + 7x$ is 3 .

Q4 (ii) Write the degree the following polynomial: $4 - y^2$

Answer:

Degree of a polynomial is the highest power of the variable in the polynomial.

Therefore, the degree of polynomial $4 - y^2$ is 2.

Q4 (iii) Write the degree the following polynomial: $5t - \sqrt7$

Answer:

Degree of a polynomial is the highest power of the variable in the polynomial.

Therefore, the degree of polynomial $5t - \sqrt7$ is 1

Q4 (iv) Write the degree the following polynomial: 3

Answer:

Degree of a polynomial is the highest power of the variable in the polynomial.

In this case, only a constant value 3 is there and the degree of a constant polynomial is always 0.

Q5 (i) Classify the following as linear, quadratic and cubic polynomial: $x^2+x$

Answer:

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $x^2+x$ with degree 2

Therefore, it is a quadratic polynomial.

Q5 (ii) Classify the following as linear, quadratic and cubic polynomial: $x - x^3$

Answer:

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $x - x^3$ with degree 3

Therefore, it is a cubic polynomial

Q5 (iii) Classify the following as linear, quadratic and cubic polynomial: $y + y^2 + 4$

Answer:

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $y + y^2 + 4$ with degree 2

Therefore, it is quadratic polynomial.

Q5 (iv) Classify the following as linear, quadratic and cubic polynomial: $1 +x$

Answer:

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $1 +x$ with degree 1

Therefore, it is linear polynomial

Q5 (v) Classify the following as linear, quadratic and cubic polynomial: $3t$

Answer:

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $3t$ with degree 1

Therefore, it is linear polynomial

Q5 (vi) Classify the following as linear, quadratic and cubic polynomial: $r^2$

Answer:

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $r^2$ with degree 2

Therefore, it is quadratic polynomial

Q5 (vii) Classify the following as linear, quadratic and cubic polynomial: $7x^3$

Answer:

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $7x^3$ with degree 3

Therefore, it is a cubic polynomial

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

1. Can we say y + 3/y is a Polynomial?

No, we can't say the given term a Polynomial, because it does not follow the fundamental definition of Polynomial

2. Is Introductory exercise exercise 2.1 in chapter 2 important?

There are a total of 5 exercises in chapter 2 i.e. Ex 2.1, 2.2, 2.3, 2.4, 2.5, hence knowledge of preceding exercise make it more effective for students to understand more.

3. What are the attached topics related to chapter 2?

Well there are many more topics like a polynomial in one variable, remainder theorem, factorization, and algebraic identities

4. Can you give an example of a monomial?

Monomial is a type of polynomial that contains only one term example = ax²

5. Can you give an example of binomial?

Binomial is a type of polynomial that contains only 2 terms example = ax² + b

6. What is the degree of polynomial x² +x?

The highest power of x² +x is 2

Therefore degree = 2 hence it is a quadratic polynomial

7. What does polynomial with degree = 4 called?

A polynomial with degree = 4 is called bi quadratic polynomial, which is not in the course of chapter 2 Class 9

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