PDF Name Polynomials – NCERT Book Class 9th Maths Chapter 2 18 1.3 MB English PDF PREVIEW

## Introduction to Class 9th Maths Chapter 2

The Class 9th Maths Chapter 2 It starts with an introduction to algebraic expressions and their factorization. The chapter then defines polynomials and their terminology, including degree, leading coefficient, and constant term. It also covers the addition, subtraction, multiplication, and division of polynomials.

The chapter then introduces the Remainder Theorem and Factor Theorem and explains how they can be used in the factorization of polynomials. Finally, Polynomials class 9 PDF discusses some algebraic identities and their use in factorization and evaluating expressions.

## What will you learn from this chapter?

In this Class 9th Maths Chapter 2, you will learn about the basics of Polynomials, including their terminology, degree, leading coefficient, and constant term. It also explains how to add, subtract, multiply, and divide Polynomials. The chapter introduces the Remainder Theorem and Factor Theorem and explains how they can be used in the factorization of Polynomials.

Additionally, the chapter discusses some algebraic identities and their use in factorization and evaluating expressions. By the end of the chapter, you will have a solid understanding of how to work with polynomials in one variable.

### What is a polynomial, and what are its components?

A polynomial is an algebraic expression consisting of variables and coefficients, with only the operations of addition, subtraction, and multiplication. Its components include terms, degrees, leading coefficients, and constant terms.

### How do you add, subtract, multiply, and divide polynomials?

To add or subtract polynomials, you combine like terms. To multiply polynomials, you use the distributive property and FOIL method. To divide polynomials, you use long division or synthetic division.

### What is the degree of a polynomial, and how is it determined?

The degree of a polynomial is the highest power of the variable in the polynomial. It is determined by looking at the variable’s exponent in the term with the highest degree.

### What is the leading coefficient of a polynomial, and how is it determined?

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. It is determined by looking at the coefficient of the term with the highest degree.

### What is the constant term of a polynomial, and how is it determined?

The constant term of a polynomial is the term that does not have a variable. It is determined by looking at the term that does not have a variable.

### What is the Remainder Theorem, and how is it used in the factorization of polynomials?

The Remainder Theorem states that if a polynomial f(x) is divided by (x-a), then the remainder is f(a). It is used to find the remainder of a polynomial when divided by a linear factor.

### What is the Factor Theorem, and how is it used in the factorization of polynomials?

The Factor Theorem states that if a polynomial f(a) is equal to zero, then (x-a) is a factor of f(x). It is used to find the factors of a polynomial.

### What are some algebraic identities, and how are they used in factorization and evaluating expressions?

Algebraic identities are equations that are true for all values of the variables. Examples include (a+b)^2 = a^2 + 2ab + b^2 and a^2 – b^2 = (a+b)(a-b). They are used in factorization and evaluating expressions.

### Can you provide an example of a polynomial and explain how to determine its degree, leading coefficient, and constant term?

An example of a polynomial is 3x^2 + 2x – 1. Its degree is 2, its leading coefficient is 3, and its constant term is -1.

### How can you use the concepts learned in this chapter to solve real-world problems?

The concepts learned in this chapter can be used to solve real-world problems such as finding the area of a rectangular field given its dimensions in terms of a polynomial expression.