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NCERT Solutions for Class 9 Maths Chapter 2 Polynomials (Ex 2.2) Exercise 2.2

## NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.2 (Ex 2.2)

NCERT Solutions for Class 9 Maths Chapter 2 teach you about polynomials. Vedantu’s NCERT Solutions for Class 9 Maths Chapter 2 PDF makes you aware of every aspect of Polynomials - be it finding value, using algebraic identities or factorization of polynomials. Our Exercise 2.2 Class 9 Maths solution explains everything about polynomials in an easy to understand way. Vedantu provides students with a Free PDF download option for all the NCERT Book Solutions of updated CBSE textbooks. Subjects like Science, Maths, Engish will become easy to study if you have access to NCERT Solution for Class 9 Science, Maths solutions, and solutions of other subjects that are available on Vedantu only.

## Class 9 Maths Chapter 2 – Exercise 2.2

Vedantu’s Class 9 Maths Chapter 2 Exercise 2.2 includes the following problems from polynomial-

- Finding the value of polynomial when the value of the variable is randomly fixed by the teacher,For example, if I ask you to find the value of 2x + 3x when I have randomly set the value of X as 5, you will put the value - 5 in place of X and then multiply 2 and 3 with 5.
- Finding whether a particular value of the variable will result in the polynomial to be equated as For example, if X equals to 5 in the equation 2X - 10, then the X = 5 is a zero of the given polynomial.
- Finding which value of the variable will result in the polynomial to be equated as 0. For example, if I want to make the value of 3X+1-7 then I have to assign the value of X as 2.

**What Are Polynomials? Constants and Variables**

Before discussing polynomials, it is necessary that you have a clear idea about variables and exponents. Consider the following equation -

2x + 3x = 10

Here we don't know at first what X is. When we solve the equation, we come to the conclusion that here X is 2. So, what X does here is it answers the ‘what’ of a question. In this equation, the question that is implied is - what should we multiply 2 and 3 with so that the addition of the product results in 10?

Again when we are confronted with the following equation -

2x + 3x = 20

the result of X changes. So, the value of X varies the situation.

This is what we call variable. This variable is generally denoted by x,y,z etc.

Again, if you look at the above two examples, the values of 2 and 3 never change. In both situations, the values of 2 and 3 remain fixed. These are called constants.

Now, look at this,

2³

Here the value of 2 increases exponentially ( 2*2*2). The power 3 is known as an exponent.

Terms

If you look at the algebraic expression - 2x + 3x - written above, you will see there are two parts in it - 2x and 3x. These parts are called terms.

Polynomial

Polynomial is a mathematical expression that has multiple terms and consists of constants, variables and non-negative or non-fractionated exponents. The polynomial will only involve addition, subtraction or multiplication.

So 2x + 3x is a polynomial in the variable X.

Again, 2³ + X³ + 3² is a polynomial.

But X + 1∕X is not a polynomial since 1/x can be written as . As said earlier, a polynomial does not allow negative exponents.

Expressions that have √X are not polynomials too since √X can be written as and we know that this is not accepted by polynomials.

If you look at the expression 2x + 3x, the numbers before the variables are called coefficients.

**Class 9 Maths Chapter 2 – Other Exercises (2.1 and 2.3)**

Here are a few other exercises that you will find in the NCERT Solutions for Class 9 Maths Chapter 2 PDF –

In this exercise of Class 9 Maths Chapter 2, students will be introduced to the concept of polynomials. They will obtain an indent knowledge regarding polynomials in one variable and how to solve the associated sums through shortcut techniques. Here are some important questions for exams that are provided in the exercise.

**Question 1**: Finding the polynomials among the expressions in one variable and stating reasons for the answers.

**Question 2**: Finding the coefficients of x2 in the provided expressions.

**Question 3**: Examples of a binomial of degree 35 and monomial of degree 100.

**Question 4:** Determining the degree of polynomials.

**Question 5**: Classifying linear, quadratic and cubic polynomial expressions.

This chapter is a continuation of Exercise 2.2 Class 9 of NCERT maths book. Students will get in-depth knowledge about the Factor Theorem by solving all questions provided in this exercise step by step.

**Question 1**: Finding the remainder when divided by expressions provided.

**Question 2:** Determining remainders.

**Question 3:** Checking if provided expressions are factors.

**How Can Vedantu Help You?**

Vedantu's Polynomials Class 9 solutions will help you understand all the topics included in the Polynomials chapter. NCERT guidelines specifically advise teachers to build the fundamental knowledge of the subjects in the students. Vedantu follows this NCERT advice thoroughly. That is why you will find not only solutions to the questions on polynomials but also the explanations on the logic behind our solutions. For example - in question number 2 of Ex 2.1 of our Polynomials Class 9 NCERT Solutions when we are asked to find the coefficients of given polynomials we showed how has an invisible 1 before it. So the coefficient of X² is 1.

Our answers in Class 9th Maths NCERT Solutions Chapter 2 include every step. No step has been skipped. You will not struggle to understand how we reached the result from a given equation. So in question 1(i) of Ex 2.2, we showed how we arrived at the answer 3 by solving the equation step by step. This will not only help the students to understand the granularities in the chapter but will also help them to get good marks.

Every Polynomial formula Class 9 has been used in our solution. The students will get to learn all the aspects of the chapter. Reading our PDF, a student can answer any question from this chapter with confidence.

The Polynomials Class 9 PDF is written in a lucid language. Apart from the Maths expressions, we have used simple, easy to understand words so that students can understand the solutions. Even the math expressions are adequately explained wherever deemed fit.

The Class 9 Maths Chapter 2 PDF has accurate solutions to every polynomials problem. The answers are written by expert teachers who know how to solve a Maths problem so that students understand the process and even the examiners get impressed by the detailed process. These teachers are well aware of NCERT guidelines and follow them to write their answers. There is no unnecessary information in our solutions.

Vedantu’s Polynomial Class 9 PDF is neatly organised. The solutions are written in an uncluttered, easy to understand way. That is why in question 1 of Ex2.3, you will find that we have used red ink to indicate the cutting off of -2x² and +2x². This visually pleasurable way of reading the solutions will help the students to maintain their focus on the solutions.

You can use our NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.2 to learn all the intricacies of polynomials. These solutions can provide you with everything that you need to excel in the chapter. The answers in our PDF are not written by part-time bloggers, but they are written by professional teachers who took care to make the solutions as helpful as possible.

The Class 9 Maths Chapter 2 Exercise 2.2 Solutions are absolutely free of cost. You don’t need to pay a single penny to download our PDF. You can simply enter your email id and we will send the download link to your email. Vedantu is not motivated by profit; we are genuinely interested in making the learning process of students better. We believe every Indian student has the right to get a quality education.

**Learn Online with Vedantu’s Online Class**

Our PDF on polynomials is exhaustive and can help you in finding solutions to all the questions asked in the textbook. Maths needs explanation - countless of times. You might want to ask questions about a particular solution in our PDF. So to help you, Vedantu holds online classes where you can ask questions directly to the teachers. This interaction is particularly necessary for understanding Maths chapters. The schedule of the classes is announced beforehand. We have helpful videos too which will help you understand the solutions in a much more easy and efficient way.

Our online teachers are experts in their subjects and come from respectable institutions like IITs. These teachers know how to teach Maths to students in such a way that students do not get bored. The teachers are aided by simultaneous images, videos and slides. This visual way of teaching ensures easy retention in students.

With our Master Class, you can experience a whole new learning experience. We are offering free seats in our master class for a limited period of time. These masterclasses can enhance your knowledge in ways you cannot fathom. We do not employ cheap tricks and tips. Our main focus is on building the basic knowledge of the students. Our Master Class is not just for advanced students, intermediate students can get benefit from the Master Classes as they will shed fear for Maths and grow a love for the subject.

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Q 1: Give a brief description of the topic.

Ans: Polynomial is acquired from the word “poly” which means “many” and the word “nominal” refers to “term”. In Math subject, a polynomial expression consists of variables which are also known as coefficients and indeterminates. The coefficients require the operations of addition, subtraction, non-negative integer exponents of variables and multiplication.

Polynomials are utterances with one or more phrases with a non-zero coefficient. A polynomial can also have one or more than one number of terms. In the form of a polynomial, each utterance in it is known as a term. Suppose x^{2} + 4x+ 2 is polynomial, then the expressions x^{2}, 4x, and 2 are the terms of the polynomial. Each term of the polynomial has a coefficient. For example, if 4x+1 is the polynomial, then the coefficient of x is 4.

Q 2: What are the important terms of a polynomial?

Ans:

A term might either be a variable or a single digit or it also could be a sequence of the variable with digits.

The degree of the polynomial is the most distinguished power of the variable in a polynomial.

A polynomial of degree 1 will be termed as a linear polynomial.

A polynomial of degree 2 will be described as a quadratic polynomial.

A polynomial of degree 3 is termed as a cubic polynomial.

A polynomial of 1 term is termed as a monomial.

A polynomial of 2 terms is termed as binomial.

A polynomial of 3 terms is termed as a trinomial.

A real number ‘a’ is a zero of a polynomial p(x) if p(a) = 0, where a is also termed as root of the equation p(x) = 0.

A linear polynomial in one variable holds an individual zero, a polynomial of a non-zero constant has no zero, and every real character is a zero of the zero polynomial.

Q 3: What are the topics that are covered in this chapter?

Ans: Polynomial is an algebraic expression which includes constants, variables and exponents. It is the expression where the variables have just certain elemental powers. The topics that are covered in this chapter are:

Introduction

Polynomials in One Variable

Zeros of Polynomials

Remainder Theorem

Factorisation of Polynomials

Algebraic Identities

Polynomial expressions are algebraic equations which will have two or more terms with the equal variables of different exponents. This is one of the notable topics for class 9 Mathematics, which students require to learn in order to gain profound knowledge about complex algebraic expressions. Mathematics is one of those subjects that serve as a foundation of numbers, analysis, figures and logic.

Q 4: Are the answers provided by Vedantu, sufficient to attain accurate marks?

Ans: Our answers are made to the point and they are drafted to aid you from the exam portion of the view. Answers to the exercising questions are certainly given with examples and they are 100% curate. Our answers will make your learning easy for the exam as they are fitted to be compatible with the tips given with the assistance of using CBSE maths Syllabus and NCERT Book.

Our answers will assist you in advancing a conceptual basis with all the principal ideas in a comprehensible language. The exercising covers all of the vital topics and subtopics of the chapter which might occur for your Class 9 maths exams. You also can clear all of your doubts from here and in this manner, you can definitely perform well in your Class 9 maths exam.