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NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials are a great study material for students. These solutions are crafted by top Maths experts at askIITians and are based on the latest syllabus for the academic year 2022. Polynomial is an interesting chapter included in the Class 9 Maths syllabus. It is based on addition, subtraction, multiplication, and division of algebraic expressions. You must have studied what algebraic expressions are in earlier classes. An algebraic expression is a combination of one or more variables and coefficients combined by any of the four algebraic operations (addition, subtraction, multiplication, and division). 

In Chapter 2 Polynomials of Class 9 Maths NCERT book, you will study polynomials. A polynomial is a type of expression in which the exponents of all variables are a whole number. For example, in this polynomial, x+5, y2+5, and 3x3−7, the exponent of x is always a positive, non-negative number. You will also learn about the remainder theorem of polynomials that are used for factorization of polynomials and some important algebraic identities for polynomials. Our free NCERT solutions for Class 9 Maths Chapter 2 Polynomials are ideal to help you understand the important concepts of this chapter. Combined with our free revision notes for Class 9 Maths Chapter 2 Polynomials, they form a complete, self-explanatory guide for students to learn the important concepts of the chapter at their own pace. 

About NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

You must take note of some of the important concepts of polynomials before you start solving the NCERT exercises of this chapter.

  • Each term in a polynomial has a coefficient. 
  • Zero Polynomial: The constant polynomial 0 is called the zero polynomial. 
  • Monomial: Polynomials having only one term are called monomials.
  • Binomial: Polynomials having only two terms are called binomials. 
  • Trinomial: Polynomials having only three terms are called trinomials. 
  • Degree of a Polynomial: The highest power of the variable in a polynomial is the degree of the polynomial. 
  • The degree of a non-zero constant polynomial is zero. 
  • A polynomial of degree one is called a linear polynomial. 
  • A polynomial of degree two is called a quadratic polynomial. 
  • A polynomial of degree three is a cubic polynomial. 
  • A zero of a polynomial p(x) is a number c such that p(c) = 0. 
  • Remainder Theorem: Let p(x) be any polynomial of degree greater than or equal to one 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 of p(x).
  • Important algebraic identities:
    • Identity I: (x + y) 2 = x 2 + 2xy + y2 
    • Identity II: (x – y) 2 = x 2 – 2xy + y2
    • Identity III: x 2 – y 2 = (x + y) (x – y)
    • Identity IV: (x + a) (x + b) = x 2 + (a + b)x + ab

Download NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

NCERT Solutions for Class 9 Maths Chapter 2 by askIITians are a smart way to learn the chapter and master all its concepts. These solutions include comprehensive answers to all the questions of the chapter. Every answer is calculated in a stepwise manner to avoid confusion. You can easily build a strong grasp of the chapter with the NCERT online solutions prepared by our qualified Maths experts. This will help you revise the chapter as per the CBSE exam pattern and syllabus and also will make you more confident for your exams. The best part is, you can download these solutions for free. 

Download free NCERT solutions for Class 9 Maths Chapter 2 Polynomials from the links given below:

  • Class 9 Maths Chapter 2 Ex 2.1 Solutions - 21 Questions
  • Class 9 Maths Chapter 2 Ex 2. Solutions - 22 Questions
  • Class 9 Maths Chapter 2 Ex 2.3 Solutions - 7 Questions 
  • Class 9 Maths Chapter 2 Ex 2.4 Solutions - 20 Questions 
  • Class 9 Maths Chapter 2 Ex 2.5 Solutions - 41 Questions 

NCERT Solutions for Class 9 Maths Chapter 2 Ex 2.1 

The first exercise of Chapter 2 Polynomials of Class 9 Maths NCERT book is based on the basic definition of polynomials, degree of a polynomial, coefficients of a polynomial, and types of polynomials like linear, quadratic, and cubic. This exercise includes 21 questions all of which are quite simple if you understand the basics of polynomials. 

For instance, in question 3 you have to give a binomial which has a degree of 35 and a monomial that has a degree of 100. In question 5, you are given 7 different polynomials and you have to classify them as linear, quadratic, and cubic polynomials. Download our NCERT solutions for this chapter real quick and start solving the exercise questions on your own. 

NCERT Solutions for Class 9 Maths Chapter 2 Ex 2.2

The second exercise of Class 9 Maths NCERT Chapter 2 Polynomials is about finding the zeros of a polynomial, verifying whether the given solutions are zeroes of a polynomial or not. To solve this exercise you must take note that:

  • A zero of a polynomial need not be 0. 
  • 0 may be a zero of a polynomial. 
  • Every linear polynomial has one and only one zero.
  • A polynomial can have more than one zero.

There are 22 questions in this exercise, all based on the above points. For instance, in question 4 you have to find the zeros of linear polynomials. You must be careful in solving this exercise and ensure that you have correctly placed the exponents and coefficients in a polynomial. Students often misplace the exponents and get a completely wrong answer. 

NCERT Solutions for Class 9 Maths Chapter 2 Ex 2.3

The third exercise of this chapter is based on a very important concept of polynomials, the remainder theorem. This theorem helps you divide one polynomial with another. This is quite a simple exercise with just 3 questions, yet you might face problems in solving them. This is why our online NCERT Solutions for Class 9 Maths are your best study guide to complete this exercise. It is important to practice more questions based on the remainder theorem for this chapter as this theorem is quite important. 

NCERT Solutions for Class 9 Maths Chapter 2 Ex 2.4

The fourth exercise of Chapter 2 Polynomials for Class 9 Maths NCERT book is based on the factor theorem or factorisation of polynomials. This exercise has 20 questions each of which is important to understand the factorization of polynomials. For example, in question 1 you have to find whether (x+1) is a factor of the different polynomials given in the question. In question 2, you have to use the factor theorem to find out whether g(x) is a factor of p(x). 

Solving his exercise is no more a difficulty for students since we have given stepwise solutions for all questions. These solutions will make it easier for you to understand how to tackle questions related to factor theorem in polynomials. Once you practice the exercise well, you can easily score full marks in this chapter. Download our free NCERT solutions today. 

NCERT Solutions for Class 9 Maths Chapter 2 Ex 2.5

The last exercise of Chapter 2 Polynomials for NCERT book includes 41 questions. You might have to apply different algebraic identities in this exercise to solve the questions. There are different types of questions in this exercise. For example, question 4 has 6 parts, you have to expand the polynomials based on different algebraic identities. In question 8 as 4 parts, you have to factorise the polynomials. 

Question 15 and Question 16 of this exercise are quite interesting. In question 15 you have to give possible expressions for the length and breadth of rectangles whose equations of areas are given to you. In question 16, you are given the volumes of 2 cuboids and you have to find the possible expression for their dimension. 

Quick tips for students while solving NCERT exercises of Class 9 Maths Chapter 2 Polynomials: 

  • Always double-check the exponents given in the polynomial. Any mistake here can lead to a wrong answer. 
  • Be very careful while you copy the polynomial from the question to your notebook. Students often misplace arithmetic operations given in a polynomial. 
  • Always check your calculations at least twice before finalising your answer since polynomials is a new concept for you. 
  • If you have any doubts, download our NCERT solutions for the chapter and refer to them at any time you want. 

Why NCERT Solutions for Class 9 Maths Chapter 2 Polynomials are Important? 

Feel Relaxed: With our online NCERT solutions, students can have the proper understanding of the chapter. They have all the solutions with them, which makes them feel relaxed as they do not have to rush to anyone to solve their doubts. 

Solidify Concepts: Our NCERT solutions for polynomials help in enhancing the conceptual understanding of the chapter. You can easily understand what is a remainder theorem, zeros of a polynomial, factor theorem, etc using our stepwise NCERT solutions. 

Learn at your Pace: The NCERT solutions for Class 9 Maths that we provide are self-explanatory. You do not need any further guidance to understand these solutions. We have explained every answer in a detailed, stepwise format. You can study them as many times as you want until everything is clear to you. 

Revise Last-Minute: Our NCERT solutions form the best last-minute revision notes for the students as they help in revising all important concepts of the chapter. You can just go through our NCERT solutions a day before the exam and ensure good marks. 

Practice: Many times students just solve a few questions from the exercise thinking that all the other questions would be the same. However, there can be a chance when you need more practice to master the concept of polynomials. With our NCERT solutions in hand, students can focus on practising all questions. 

With so many benefits, NCERT solutions for Class 9 Maths Chapter 2 Polynomials are a must for students. Download our solutions right away and start practising the important concepts of the polynomial chapter easily. 

NCERT Solutions for Class 9 Maths Chapter 2 FAQs

  1. What are the different ways to factorise a polynomial? 

Exercise 2.4 of Chapter 2 Polynomials is based on factorisation. There are different ways to factorise a polynomial such as Method of Common Factors, Grouping Method, Factoring by splitting terms and Factoring Using Algebraic Identities. 

  1. Can we add and subtract polynomials?

Yes, you can add or subtract one polynomial from another. You must take care of the like terms while adding or subtracting. You only need to add or subtract the coefficients keeping the like terms as it is. Check out our online video lectures on polynomials for better understanding. 

  1. What are the four major types of a polynomial?

Based on its degree, a polynomial can be categorised as Zero or Constant polynomial, Linear polynomial, Quadratic polynomial, and Cubic polynomial. 

  1. Can I find Class 9 Maths NCERT solutions for other chapters also?

Yes, we have provided complete solutions for all the chapters of the textbook so that students do not have to go anywhere else. Find complete guidance here at askIITians for Class 9 Maths. 

  1. Is the NCERT book enough for exam preparation?

CBSE exams are based on the NCERT textbooks only. However, if you have time and want to test your knowledge about the chapter, you can use additional reference books for practice. Using such books will further solidify your Maths concepts. 


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