NCERT Solutions for Class 9 Maths Chapter 2 Polynomials
Here We have given NCERT Solutions for Class 9 Maths Chapter 2 Polynomials. These solutions are posted very carefully without any errors.
You may already be familiar with the concepts of variables and constants, and solving equations with them. For instance, finding the value of the variable in an equation or applying the algebraic identities to them.
Table of Contents
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.1
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.2
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.3
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.4
Class 9 Maths NCERT Solutions Chapter 2
Class 9 NCERT chapter 2 solutions will require you to recall these concepts to build up on them and understand the new concepts associated with polynomials. As a refresher polynomials are expressions made of constants, variables and exponents which are related via arithmetic operators. 2x + 1, is a polynomial but more specifically it is a linear polynomial in one variable with 2 being the coefficient of the variable x. The above polynomial has two terms i.e. 2x and 1.
Additional requirements include: The terms in the polynomial must have whole number exponent values so x + x1/2 is not a polynomial and there are only a finite number of terms in them.
Key terms in Chapter 2 – polynomials
- Constant polynomial: A polynomial having only the constant and no variable for instance p(x) = 2 is a polynomial as well.
- Degree of the polynomials: The highest exponent in the polynomial. It is always zero for a non-zero constant polynomial. One having degree 2 is called quadratic, and one with degree 3 is a cubic polynomial.
- Polynomials in multiple variables: Some polynomials may have more than one variable for instance p(x) = 4x + 3y or 7z +21x + 35y.
- Zeros of a polynomial: The value of the variable in the polynomial that is obtained by equating the polynomial to 0. In the equation f(x) = 2x +1, f(-1/2) gives 0 so we can say that -½ is a 0 of the polynomial 2x + 1.
In simple terms the remainder theorem states that a polynomial that is p(x) (a polynomial of degree >= 1) is divided by x-a (where a is any real number) then the remainder will be p(a). This definition may need a lot of work and a thorough understanding of some fundamental ideas to understand properly. In NCERT Class 9 maths solutions, this may arguably be one of the trickiest concepts to grasp purely because of the length of the explanations given in the text. Just remember the following :
- The number being divided is the dividend and the number dividing is the divisor. The quotient is the answer given from the division and the remainder if any remaining value that occurs when the dividend is not exactly divisible by the divisor.
- In 12 ፥ 5, 12 is the dividend, 5 is the divisor, 2 is the quotient and 2 is the remainder.
- Dividend = (Divisor * Quotient) + Remainder
- Additionally if Remainder = 0, then the Quotient is a factor of the divisor.
- These concepts can also be extended to two polynomial equations.
- The equation 2×2 + x = x(2x+1)so x and 2x +1 are the factors of the equation
When going through NCERT solutions for chapter 2 polynomials we suggest keeping the points in mind when doing the examples because it will make understanding the examples much easier.
Factor Theorem of Class 9
The remainder theorem acts as the proof for the factor theorem, which is signified by the definition: If a polynomial p(x) of degree n>=1 and a is any real number then x-a is a factor of p(x) if p(a) = 0. Additionally, for quadratic polynomials in particular you can obtain the factors by splitting the middle terms . There are several questions in the exercises that use the factor theorem in various ways and doing all the problems therein will be highly beneficial for fully understanding the concept.
FAQs (Frequently Asked Questions)
How many exercises are in NCERT Solutions for Class 9 Maths Chapter 2?
There are 5 rather sizable exercises in the NCERT Maths class 9 chapter 2 and each one will allow you to become more proficient at different concepts introduced throughout the chapter. Some questions will include finding missing values given a polynomial and its factor, some will ask you to identify the type of polynomial, and some will enquire about the remainder of a polynomial if its divisor is given.
Why are Class 9 Maths NCERT Solutions Chapter 2 Important?
This chapter represents a particular increase in difficulty for most students entering class 9 because it introduces a large number of concepts at once because they are all interrelated. So students may frequently encounter problems in understanding the concept or attempting the questions. Because of these challenges, we provide you the step-by-step detailed solutions for NCERT Class 9 Maths exercises so that you may become better at learning how to solve the questions and become more familiar with the type of questions you can expect in the exams.
What is a Polynomial?
Polynomials are expressions in algebra characterized by the presence of variables and coefficients. These variables, indeterminates, can be manipulated using various arithmetic operations like addition, subtraction, and multiplication. Polynomial expressions also allow for the use of positive integer exponents.
Are NCERT Solutions for Class 9 Maths Chapter 2 difficult to learn?
Seeing the sheer amount of information laid out in this article you may be intimidated by the prospect of having to learn everything. However, once you get over your own misgiving the chapter is rather intuitive. It builds up on things that have already been taught and the absolute best way to practise it is via doing each example yourself and giving multiple tries to problems you struggle with; with each trial, you will become much better at answering the questions.
So fret not whenever you do get stuck we have the solutions for Class 9 Chapter 2 polynomials ready to go. We hope you will gain greatly from the resources we provide.
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