NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials will aid you in understanding Polynomials and the terminologies associated with them. In Chapter 2 of NCERT Solutions for Class 9 Maths, you will learn the application of new algebraic identities for the factorization and evaluation of algebraic expressions. You will also study some new concepts such as the Remainder Theorem and Factor Theorem. Some previously introduced concepts are also discussed in this Chapter such as addition, subtraction, multiplication, and division and factorization of Polynomials.
NCERT Class 9 Maths Chapter 2 Polynomials includes 5 exercises with 33 questions. All these questions cover the concepts of Chapter comprehensively. The exercise questions in this Chapter are mostly subjective in nature but some of them require just brief answers comprising a line or two. These questions are sufficient for you to practice before CBSE exams. Solving NCERT exercise questions will be helpful for you as you will be able to ace the topics that require rigorous practice such as factorization of Polynomials.
NCERT Solutions for Class 9 Maths Chapter 2 by Instasolv comply with the latest CBSE guidelines. These NCERT Solutions include step by step explanations and will help you understand the process of solving questions. Practising the questions giving in NCERT Class 9 Maths Book will not only help you in CBSE exams but also in national level competitive examinations and olympiads.
Important Points of NCERT Solutions for Class 9 Maths Chapter 2 Introduction
- The algebraic expressions that have only whole numbers as the exponents of their variable are known as Polynomials.
- The different components of a polynomial separated by a plus or minus sign are known as terms of the polynomial.
- Each term of a polynomial has a constant in multiplication with the variable, which is called a coefficient.
- Integers are examples of constant Polynomials. The constant polynomial 0 is called the zero polynomial.
- Polynomials having only two and three terms are called binomials and trinomials respectively.
- We call the highest power of the polynomial as the degree of the polynomial. The degree of a non-zero constant polynomial is zero. Polynomials of degree two and three are known as quadratic and cubic Polynomials respectively.
- A polynomial in one variable x of degree n can be expressed in the form.
anxn+ an-1xn-1 + … + a1x + a0
Where, a0, a1, a2, …, an are constants and an ≠ 0,
If an= 0, then we get the zero polynomial, the degree of which is not defined.
Zero of a Polynomial
- Zero of a given polynomial, p(x) is a number c, such that p(c) = 0
- A non-zero constant polynomial such as ‘5’ has no zero whereas, by conventions, all Real numbers are zeroes of the zero polynomial.
- There is one and only one zero of a linear polynomial.
- 0 may be a zero of a given polynomial but not necessarily.
- A polynomial can have one or more than one zero.
Remainder Theorem and Factor Theorem
Dividend = (Divisor x Quotient) + Remainder
So, if p(x) and g(x) are two Polynomials with degree of p(x) ≥ g(x), then Polynomials
q(x) and r(x) can be found such that:
p(x) = g(x)q(x) + r(x),
where degree of r(x) < degree of g(x)
r(x) and q(x) represeny remainder and quotient respectively.
Remainder Theorem: Let p(x) be any polynomial of degree 1 and let a be any real number. If p(x) is divided by the linear polynomial x-a, then the remainder is p(a).
Factor Theorem: If p(x) is a polynomial of degree n > 1 and a is any real number, then (i) x-a is a factor of p(x), if p(a)= 0; and (ii) p(a) = 0, if x-a is a factor p(x).
Highlights of NCERT Class 9 Chapter 2 Polynomials
- Polynomials of one, two and three terms are called monomials, binomials and trinomials respectively.
- Every linear polynomial in one variable has only 1 zero.
- Linear, Quadratic and cubic Polynomials have degrees 1, 2 and 3 respectively
- Identities can be used split terms for factorization with the help of factor theorem.
Discussion of Exercises of NCERT Solutions for Class 9 Maths Chapter 2
- The first exercise of NCERT Solutions for Class 9 Maths Chapter 2 Solutions asks you to write down examples of the different types of algebraic expressions. It also contains questions where you will be able to identify the number of terms and degree of the polynomial.
- In further NCERT exercises, you will have to recall the division of algebraic expressions. Our step-by-step Solutions have explained that in detail.
- The answers demand you to use the theorems learned in this Chapter for various questions.
- You will be able to arrive at the answers of some questions such as factorization of some complex Polynomials, with the help of the algebraic identities given in this Chapter.
Why NCERT Class 9 Maths Chapter 2 Solutions prepared by Instasolv are Important?
- You will find instant Solutions to all your doubts while going through this set of CBSE NCERT Solutions as they are prepared by our expert team which is dedicated to making Class 9 Maths simpler for you.
- NCERT Solutions for Class 9 Maths Chapter 2 will help in substantial improvement in your CBSE exam scores.
- We, at Instasolv guarantee, to save your time and help you utilize your time efficiently by keeping note of all the major points where you might stumble.
- You can totally rely on these NCERT Solutions as they are error-free and are on-point according to the CBSE syllabus.