NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

 

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials include 4 exercises and 13 questions. The polynomials chapter of Class 10 Maths is based on zeros of a polynomial, the relationship between zeros and the coefficients of a polynomial, and the division algorithm for polynomials. The NCERT questions of this chapter include finding the number of zeros of the given polynomial functions, finding the zeros of quadratic polynomials and verifying the relation between the zeros and the coefficients, dividing the polynomials and finding their quotient and remainder. 

 

We, at askIITians, have created exercise-wise solutions for all the four exercises of this chapter to help students resolve their doubts and clarify their concepts. The solutions are based on the latest CBSE exam pattern to help students prepare for the Class 10 Maths board exam. Let us see what has been included in Chapter 2 of Class 10 Maths and how you can download the NCERT Solutions for this chapter from the askIITians website. 

About NCERT Class 10 Maths Chapter 2 Polynomials 

• Polynomial: A polynomial is a type of algebraic expression with variables, constants, and exponents combined using arithmetic operations like addition, subtraction and multiplication. 
• Degree of a Polynomial: The highest power of x in the polynomial p(x) is called its degree. For example, the degree of the polynomial 3x3 + 2x2 + 4x + 10 = 0 is 3. ​
  • Cubic Polynomial: A polynomial with degree 3 is called a linear polynomial. 
  • Quadratic Polynomial: A polynomial with degree 2 is called a linear polynomial. 
  • Linear Polynomial: A polynomial with degree 1 is called a linear polynomial. 
• Zeroes of a Polynomial: A real number c is known to be a zero of a polynomial p(x) if p(c) = 0. 
• Zeroes of a Linear Polynomial: The zero of linear polynomial p(x) = ax+b is -b/a or - Constant Term of p(x) / Coefficient of x 
• Zeroes of a Quadratic Polynomial: 
  • ​The general form of quadratic polynomial ax2 + bx +c where a ≠ 0 has two zeroes
  • Product of zeroes = c/a = Constant term/ Coefficient of x2.
  • Sum of zeroes = -b/a = - Coefficient of x/ Coefficient of x2.
• Zeroes of a cubic polynomial: 
  • The general form of a cubic polynomial ax3 + bx2 +cx + d where a ≠ 0 has three zeroes. 
  • Sum of zeroes = b/a = - Coefficient of x2/ Coefficient of x3.
  • Sum of the product of zeroes taken two at a time = c/a = Coefficient of x/ Coefficient of x3.
  • Product of zeroes = -d/a = - Constant term/ Coefficient of x3.
  • Division Algorithm of Polynomials: The division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that:

p(x) = g(x) q(x) + r(x), 

where r(x) = 0 or degree r(x) < degree g(x).

• The Division Algorithm of Polynomials:

For any polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that:

p(x) = g(x) q(x) + r(x), 

where r(x) = 0 or degree r(x) < degree g(x).

• Steps involved in dividing one polynomial by another:

Step 1: First, you have to obtain the first term of the quotient. For that, you need to divide the highest degree term of the dividend by the highest degree term of the divisor. Then you can carry out the division process. What remains becomes the new dividend. 

 

Step 2: Now, you have to divide the highest degree term of the new dividend by the highest degree term of the divisor and obtain the second term of the quotient. 

 

Step 3: This process goes on until you get a new dividend whose degree is less than the given divisor and you cannot divide the polynomial any further. 

 

You can also check whether your answer is correct or not by using the formula: 

Dividend = Divisor × Quotient + Remainder

Download Free NCERT Class 10 Maths Solutions for Polynomials 

 

Learn new concepts of Polynomials easily with the help of our detailed NCERT Solutions for Class 10 Maths Chapter 2 Polynomials. There are 4 exercises in this chapter, each focusing on certain concepts related to Polynomials. Let us see what is included in each exercise: 

 

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.1

The first exercise of the Polynomials chapter is based on the introduction to Polynomials and the geometrical meaning of zeroes of a polynomial. This includes topics such as the definition of polynomial, zeros of a polynomial, and the degree of a polynomial. There is only one question in this exercise. But, you must understand all the above-mentioned concepts thoroughly using our revision notes and practice questions. 

 

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

The second exercise of this chapter is based on the relationship between zeroes and coefficients of a polynomial. There are two questions in this exercise. In the first question, you have to find the zeros of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. In the second question, you have to find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

 

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3 

The third exercise of this chapter deals with the concept division algorithm of polynomials. This is an important topic from the exam perspective. You must practice all the 5 questions of this exercise and learn how to divide one polynomial by another. We have provided stepwise solutions to all the questions of this exercise. Download them in PDF form for free from our website.

 

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.4 

The last exercise of this chapter is a miscellaneous exercise based on all the concepts that you have learned in this chapter. This exercise is not from the exam perspective but it is important for you as it tests your knowledge about the chapter. The questions included in this exercise are of advanced level so you must check our NCERT Solutions for this exercise. 

 

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Benefits:

 

• All the NCERT Solutions are available for free. You can download them and study at any time. 
• The solutions include stepwise solutions to help you understand how to solve the exercise questions in the exam. 
• You can use these solutions to resolve your doubts regarding the chapter and revise all the main topics quickly before the exam. 
• You can practice at your own pace by downloading the NCERT solutions for Class 10 Maths Polynomials. 

NCERT Class 10 Maths Chapter 2 Polynomials FAQs

 

• How many examples are there in Chapter 2 Polynomials of Class 10 Maths? 

There are 9 solved examples and 13 unsolved problems in NCERT Class 10 Maths Chapter 2 Polynomials. You can download the stepwise solutions for all exercise questions from the askIITians website. 

 

• I need more study material for Chapter 2 Polynomials of Class 10 Maths. What should I do?

askIITians Maths experts have created the best study resources for the Class 10 Maths Polynomials chapter that will help you practise its concepts thoroughly. These include revision notes, NCERT Solutions, extra questions, practice worksheets, mind maps, flashcards and more. Download them from our website and start learning. 

 

• Is the NCERT book enough for board exam preparation? 

CBSE Class 10 Maths board exam is based on the NCERT book only. So it is recommended that you must solve the NCERT exercises for every chapter. You can use additional study materials for solidifying your conceptual understanding but make sure that they are based on the Class 10 Maths NCERT textbook only.