 For exam preparation, get the NCERT Solutions for class 10 Maths chapter 2 Polynomials all exercises in Hindi and English medium modified and updated for session 2023-24. According to new rationalised syllabus and latest NCERT textbooks issued for academic year 2023-24, there are only two exercises in chapter 2 in class 10th mathematics syllabus.

• ## Class 10 Maths Chapter 2 Solutions for CBSE Board

• ### Class 10 Maths Chapter 2 Solutions for State Boards

Class 10 Maths Chapter 2 Polynomials, covers various important concepts related to polynomial equations. Here are the main points to learn from this chapter. Understand what polynomials are and their characteristics. A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, with non-negative integer exponents. Learn how to determine the degree of a polynomial based on the highest power of the variable term. Identify polynomials as constant, linear, quadratic, cubic, etc., based on their degree. The ratioinalised textbooks issued by NCERT shows that there are only two exercises in chapter 2 of 10th mathematics. Earlier there were four exercises but the exercise 2.3 and 2.4 are deleted now. So, students have to practice only exercise 2.1 and 2.2 for the board exams. According to new syllabus and books issued for new session, the course structure of class 10 chapter 2 is as follows:
Zeros of a polynomial. Relationship between zeros and coefficients of quadratic
polynomials.

1. Now, Number of Exercises: 2
2. Number of Periods needed: 8
3. Weightage of Maths: 4 – 5

Know how to add and subtract polynomials by combining like terms. Understand the process of multiplying polynomials using the distributive property. Learn how to use the FOIL method for binomial multiplication (First, Outer, Inner, Last). Multiply a monomial by a polynomial and apply the distributive property. Recognize and apply formulas for special products such as the square of a binomial (a + b)² and the difference of squares (a² – b²).

 Class: 10 Mathematics Chapter 2: Polynomials Number of Exercises: 2 (Two) Content: Textbook and Extra Questions Content Type: Text, Images and Videos Academic Session: Year 2023-24 Exams Medium: English and Hindi Medium

### NCERT Solutions for class 10 Maths chapter 2

UP board Students, who are using NCERT Textbooks for their final exams, they can download UP Board Solutions for Class 10 Maths Chapter 2 from this page in PDF format. Assignments and Revision tests are given below in the format of PDF file.

Study polynomial division using long division and synthetic division methods.
Understand the concepts of divisors, dividends, quotients, and remainders. Learn techniques for factoring polynomials, including common factors, grouping, and the use of algebraic identities. Factorize quadratic trinomials of the form ax² + bx + c.

Familiarize yourself with important algebraic identities, such as (a + b)², (a – b)², and a² – b². Understand the Remainder Theorem, which relates the remainder of polynomial division to the value of the polynomial at a given point. Know the Factor Theorem, which states that (x – a) is a factor of a polynomial if and only if the polynomial evaluates to zero at x = a. All the solutions are in Hindi as well as English Medium format. Videos related to each exercises are also given below with complete explanation and examples. Students Download Class 10 NCERT Solutions Apps 2023-24 for offline use. Download here Bahupad ki prashnavali 2.1 and 2.2. Solutions are available in Hindi and English. Visit to Discussion Forum to ask your doubts and share your knowledge with the other users. For any education help, you can contact us without any hesitation.

Learn how to use synthetic division for polynomial division, particularly for dividing by linear divisors of the form (x – a). Apply polynomial equations to real-world problems and mathematical modeling. Solve polynomial equations, both linear and quadratic, by factoring and applying the zero-factor property. Understand the graphical representation of polynomial functions and how to find the roots or solutions by analyzing the graph. • #### Class 10 Maths Chapter 2 Practice Tests with Answers According to real-time information, and the knowledge based on information available up to session 2023-24, we provide specific information about the availability of study materials for Class 10 Maths Chapter 2 Polynomials at Tiwari Academy website and Apps.
Summarize the key concepts, formulas, and techniques learned in this chapter for quick reference. These are the main points to learn from Class 10 Maths Chapter 2 Polynomials. It is a fundamental chapter in algebra that serves as a basis for more advanced topics in mathematics.

### What do you understand by a Polynomial as per Class 10 Maths Chapter 2?

An algebraic expression, in which variable(s) does (do) not occur in the denominator, exponents of variable(s) are whole numbers and numerical coefficients of various terms are real numbers, is called a polynomial.

In other words,

1. No term of a polynomial has a variable in the denominator;
2. In each term of a polynomial, the exponents of the variable(s) are non-negative integers and
3. Numerical coefficient of each term is a real number.

The terms of a polynomial, having the same variable(s) and the same exponents of the variable(s), are called like terms. A polynomial of degree 2 is called a quadratic polynomial. The degree of a non-zero constant polynomial is taken as zero. When all the coefficients of variable(s) in the terms of a polynomial are zeros, the polynomial is called a zero polynomial. The degree of a zero polynomial is not defined.

### Do you know what is a monomial?

An algebraic expression or a polynomial, consisting of only one term, is called a monomial.

### Which type of polynomial is called a binomial?

An algebraic expression or a polynomial, consisting of only two terms, is called a binomial.

### Which type of algebraic expression is known as trinomial?

An algebraic expression or a polynomial, consisting of only three terms, is called a trinomial.

Tiwari Academy and similar educational websites often provide NCERT solutions and study materials to assist students in their preparation. The reasons for using Tiwari Academy platforms for NCERT solutions includes in simplified format. This platform offers comprehensive solutions that cover all the exercises and examples from the NCERT textbook, making it easier for students to understand and practice.

Many platforms provide step-by-step explanations for solving problems, helping students grasp the concepts more effectively. But they provide best and confined to current syllabus. In addition to NCERT solutions, Tiwari Academy platforms often offer additional practice questions and exercises to help students gain confidence and excel in their studies.

Online resources like Tiwari Academy are easily accessible, allowing students to study at their own pace and convenience. These platforms may also provide supplementary materials such as video tutorials, quizzes, and sample papers to enhance learning. Tiwari Academy and similar platforms may offer study materials and solutions for a wide range of subjects and topics, making them a one-stop destination for students’ academic needs.

#### 10th Maths Chapter 2 Solutions Class 10 Exercises solutions are solved in both English as well as Hindi medium in order to help all type of students following latest CBSE Syllabus 2023-24. In prashnavali 2.1 and 2.2 Ganit Solutions, if there is any inconvenient to understand, please inform us, we will short out at our level best.

If you are considering using Tiwari Academy or a similar platform for Class 10 Maths Chapter 2 Polynomials, I recommend visiting their website and exploring the available resources to see and get it as per your learning needs and preferences. Additionally, you can seek recommendations from teachers or peers to determine the quality and effectiveness of the materials provided by such platforms.

##### Zeros of Polynomials

The value(s) of the variable for which the value of a polynomial in one variable is zero is (are) called zero(s) of the polynomial. To verify the relationship between the zeroes and coefficients of a given quadratic polynomial, we can find the zeroes of p(x) by factorisation. By taking sum and product of these zeros, we can verify the following results. An elegant way of dividing a polynomial by a liner polynomial was introduced by Paolo Ruffin in 1809. His method is known as Synthetic division, which facilitates the division of a polynomial by a linear polynomial or binomial of the form x – a with the help of the coefficients involved.

Determining the zeros of polynomials, or finding roots of algebraic equations is among the oldest problems in mathematics. The modern way, we use today only developed beginning in the 15th century. Before that, linear equations were written out in words.

###### What is the History of the mathematical notations?

1. The use of the equal to (=) sign is in Robert Recorde’s book (The Whetstone of Witte in 1557). Plus sign (+) the sign of addition, minus sign (−) the sign of subtraction and the use of an alphabet for an unknown variable in Michael Stifel’s book (Arithemetica integra in 1544).

2. René Descartes, in 1637, introduced the concept of plotting the graph of a polynomial equation. Just because of him, the popularity of use of letters of the alphabet to denote constants and letters from the end of the alphabet (x, y, z, etc.) to denote variables (like 2x, 3y, 7z, etc.) in the general formula for a polynomial in one variable. ### How to make good Practice in Class 10 Maths Chapter 2 Polynomials?

Polynomials are said to be one of the important sections of mathematics, especially for Algebra. They’re used in most of the equations and topics of numerical operation in standard 10 and higher also. It wouldn’t be wrong, if we say polynomials are Building Blocks of Maths expressions. Here we will learn about how to solve all exercises of 10th Maths chapter 2. Before learning about the polynomial equation, we have to know its significant importance that makes the topic more interesting. Many Maths process that are done in everyday life can be interpreted as polynomials. With the help of polynomial equations, one can calculate the grocery bill for small and even distance travelled by light in space.

#### Step 1: NCERT Solutions for Class 10 Maths Chapter 1 with basic knowledge of Polynomial. The NCERT Solutions for Class 10 Maths Chapter 2 with basic knowledge are helpful to prepare a solid base. We understand the significant importance of learning equations. Not just for sake of scoring good marks in class 10th Board exams for better understanding also. Few equation had been first solved in 1540 by Ludovico Ferrari. Most of his work is not included in the syllabus of 10th Maths Chapter 2. Exercise 2.1 is based on zeroes of a polynomials. Here we will learn to find the zeroes of Polynomials using the intersections on x-axis. In class 10th NCERT books expect you to master the strategy to recognize with the input of formulae and solve it. This strategy must be learnt to obtain the answer to the polynomial equation. In terms of the solution of the cubic equations or the other methods you follow.

#### Step 2: Class 10 Maths chapter 2 solutions with relationship between zeros and coefficient of variables. Class 10 Maths Chapter 2 NCERT Solutions contains the relationship between zeros and coefficients. In class 10th Maths Exercise 2.2, we have to relate the coefficient of variable with the zeros. In this exercise or such cases keep them interested to find new ways to solve it while keeping the interest alive is a daunting task. This is why our NCERT Solutions for class Maths 10 contain various representations. These solutions to students addressing their different learning styles. Different videos and PDFs representations include using manipulative, showing tips, videos, presenting the problems, solving and showing symbolic offerings. For instance, in ideal classrooms, teachers show various ways to solve the same problem, whether cubic, quadratic equations, or some other. Students are being encouraged to solve them with their creative styles. It is only when there are exposed to all the various methods before.

#### Step 3: NCERT Class 10 Maths Chapter 2 solutions to prove an irrational number as irrational. The NCERT Solutions Class 10 Maths Chapter 2 is easy to solve and understand. Here, in 10th Maths Exercise 2.3, we learn the ways to prove a number as irrational if it is. Most High school students are struggling to prepare to face the most important exam as this decides their future studies. While preparing the NCERT solution for Class 10th Maths third exercise, must learn about the facts related to an irrational numbers. A lot of students memorized the polynomial, quadratic formula in middle school. But have you ever tried the cubic formula? It is quite complicated and not nearly as easy to derive if you are now aware about the relational between roots and coefficient. But if get to learn with us you will delve deeper into solving equations. This will make you confident in questions related to 10th Maths Exercise 2.3.

#### Step 4: Class X Maths Chapter 2 solution help to identify the terminating and non-terminating decimals. Class 10 Maths NCERT Book Chapter 2 solution explains about the terminating and non-terminating decimals. If we learn the concepts systematically, it quite easy to understand about terminating or non-terminating rational numbers. If this is possible we would always be able to demonstrate the application of all the equations in daily life as a polynomial. In the real world, that can be eye-opening for the students if they relate the Maths work with day to day activities. When concepts cannot be demonstrated in that manner, we can still show how it is can work in Maths. This is possible only when you are interested to know about the development of the method over time. This is why the NCERT Maths class 10th chapter contains fragments of famous mathematicians’ history. Watching videos of such terms might take a few minutes but are effective practices.

#### Step 5: Class 10 Maths Chapter 2 need to build Structural Approach towards Learning. To get the solutions of class 10 Maths chapter 2, students need a Structural Approach. We are here at Tiwari Academy to understand the value of time for scholars, who is about doing extra efforts to delve deep into studies. Keep the objective of learning clear. That can help you in a quick formative assessment to determine the knowledge you gain. You will know where the lesson will go next time. Always revise the chapter in a sufficient interval of time. We understand the importance of focus during the preparation. This is why you should get our PDF and video and work offline. Some students like more physical work than reading to understand concepts but the polynomial equations are all about the writing practice until perfection. We suggest you practice the 10th NCERT Maths MCQs, exemplar, and practice papers so that you can reinforce the knowledge.

### What are real life applications of class 10th mathematics chapter 2?

Some real life applications of class 10th mathematics chapter 2 (Polynomials) are:

1. Polynomials can be used to model different types of situations, like in the stock market to see how prices will vary with time.
2. In physics also polynomials are used to describe the trajectory of projectiles.
3. Polynomials used in industries and construction field also.
Polynomials are useful for every person and in every field.

### How many exercises, questions and examples are there in chapter 2 of 10th Maths?

There are in all 2 exercises in class 10 mathematics chapter 2 (Polynomials).
In first exercise (Ex 2.1), there is only 1 question having 6 parts.
In second exercise (Ex 2.2), there are 2 questions and each question have 6 parts.
So, there are total 3 questions in class 10 mathematics chapter 2 (Polynomials).
In this chapter there are in all 9 examples. Example 1 is based on Ex 2.1, Examples 2, 3, 4, 5 are based on Ex 2.2.

### Which questions and examples are important in Class 10 Maths Chapter 2?

In first exercise (Ex 2.1) there is only 1 question with 6 parts and all the part of this question are equally important. In second exercise (Ex 2.2) all questions are important.
Important examples of chapter 2 (Polynomials) class 10th mathematics are example 1, 2, 3, 4, 8, 9.

### What should we recall before starting chapter 2 of 10th Maths?

Before starting class 10th mathematics chapter 2 (Polynomials), students should recall chapter 2 (Polynomials) of class 9th mathematics.

Last Edited: December 9, 2023
Content Reviewed: September 25, 2023 Content Reviewer

### Sushant Mukherjee

Providing help in science for class 6 to 10. Adviser in Tiwari Academy for the science related subjects subject as well as videos contents. Ample teaching experience in schools. I am not only working for Tiwari Academy but also provide new ideas for the website and apps.