NCERT Solutions for class 9 Maths Chapter 2 Exercise 2.1 Polynomials - PDF Download

NCERT solutions class 9 maths chapter 2 ex 2.1 Polynomials, provides an overview of the fundamental concept of the polynomial and the components that form it. Students will be presented with a brief revision of terms such as variables, constant, term, and coefficient. The chapter begins with a single variable concept that is represented by a polynomial, and progresses to the introduction of fundamental terms such as monomials, binomials, linear equations and quadratic equations.

NCERT solutions class 9 maths chapter 2 ex 2.1 consists of 5 questions. Class 9 maths chapter 2 exercise 2.1 NCERT solutions Polynomials, can be downloaded in an easy-to-understand pdf format from eSaral for solving questions related to polynomials in one variable. 

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Topics Covered in Exercise 2.1 class 9 Mathematics Questions

NCERT solutions class 9 maths chapter 2 ex 2.1 covers topics related to polynomials in one variable which has been explained by our subject experts.

1. Polynomials in One Variable - A polynomial is an expression that contains one or more terms with non-zero coefficients. Polynomials can have more than one term.  

Download the book and check the equation in the summary given at the end of chapter 2 polynomials. Link to download the book: Class 9 Math Book 

A polynomial p(x) in one variable x is an algebraic expression in x of the form

 p(x)=anxn+an-1xn-1+...+a2x2+a1x+a0,

Where a0,a1, a2..., an are constants and an0

 a0,a1, a2..., an are respectively the coefficients of x0,x,x2,. . .,xn, and n is called the degree of the polynomial. Each of anxn, an-1xn-1,..., a0,with an0, is called a term of the polynomial p(x).

 2. Important Points

• Term - Each expression in a polynomial is referred to as a term. For example, if we  have a polynomial of x2+5x+2, then we can think of these expressions as the terms "x2", "5x", and "2".
• Coefficient - Each term of a polynomial is associated with coefficient. For ex. if the polynomial is 2x + 1, the x’s coefficient is 2.

3. Types of Polynomial 

1. A polynomial of one term is called a monomial. Ex. 2x
2. A polynomial of two terms is called a binomial. Ex. 5x + 2
3. A polynomial of three terms is called a trinomial. Ex. 2x + 5y – 4

4. Constant Polynomial

You can also use real numbers as a polynomial. For example, 3, 6 and 7 are polynomials without any variable. These are known as constant polynomials. The constant polynomial 0 is known as zero polynomial. The exponent of a polynomial is a whole number. For example, x-2+5x+2 is not a polynomial because the exponent of x is negative- 2, which is not a whole number.

5. Degree of a Polynomial

The highest power of the polynomial is called the degree of the polynomial.  For example, inx4+y4+4xy(x+y), the degree of the polynomial is 4. For a polynomial whose constant value is non zero, the degree shall be zero. 

There are a variety of other polynomials, including:

1. A polynomial of degree one is called a linear polynomial.
2. A polynomial of degree two is called a quadratic polynomial.
3. A polynomial of degree three is called a cubic polynomial

Tips for Solving Exercise 2.1 class 9 chapter 2 Polynomials

NCERT solutions class 9 maths chapter 2 ex 2.1 is a useful starting point in understanding the subject of polynomials. Here are some important tips to solve ex 2.1 class 9 maths.

1. The students are encouraged to revise the fundamental definitions of polynomials and their elements, which will facilitate the progress of ex 2.1 in a more efficient and expeditious manner.
2. NCERT solutions for class 9 maths chapter 2 ex 2.1 includes fundamental questions concerning variables, constants, and coefficients, as well as the degree of a polynomial and the types of polynomial expression. 
3. Students are encouraged to practice the examples provided in NCERT solutions before  solving the ex 2.1 questions.

Importance of Solving Ex 2.1 class 9 Maths chapter 2 Polynomials

NCERT solutions class 9 maths chapter 2 ex 2.1 contains a topic of polynomials in one variable. This topic is important to learn before solving ex 2.1 questions. 

1. If students are able to solve each of the questions in this ex 2.1 class 9 maths, they will be ready to understand the actual concept offered on Polynomials in class 9 maths chapter 2 ex 2.1.
2. These NCERT solutions, which have been developed by our subject experts, will give you the confidence to score high marks in exams.
3. The NCERT solutions provided by our mathematics experts team cover all the important questions from the examination perspective.
4. NCERT solutions include step-by-step explanation of each of the answers to the questions in the exercise.

Frequently Asked Questions

Question 1. What is the degree of a polynomial?

Answer 1. The highest power of the polynomial is called the degree of the polynomial. For example  in the polynomial 3x7-4x6+x+9 The degree of the polynomial is 7.

Question 2. What do you understand by binomial in class 9 maths chapter 2 ex 2.1?

Answer 2. A polynomial of two terms is called a binomial. For example: p(x) = x + 1