Latest Updates
Download: Class 10 Mathematics Important Questions
Download: Previous Year Question Paper Class 10
Download: Sample Paper Class 10 CBSE 2025-26
Download: Class 10 Syllabus 2025-26
Check Now: Class 10 Mathematics Revision Notes
NCERT Solutions Class 10 Maths Chapter 2 Polynomials
Mathematics plays a crucial role in the Class 10 curriculum, serving as a key subject for building a solid foundation for higher studies. Chapter 2 of Class 10 Maths focuses on polynomials, helping students understand essential concepts for advanced learning. NCERT Solutions for Class 10 Maths Chapter 2, created by expert mentors at Bookflicker, offer valuable guidance for mastering this chapter. You can download the Polynomial Class 10 PDF solutions for free and access them offline for your convenience.
This chapter explores various types of equations and their components, making it easier for students to grasp key ideas and tackle exercise problems. With the help of NCERT Solutions, you can effectively learn and practice new concepts. Bookflicker provides solutions for all subjects and grade levels to support students in their academic journey.
Table of Contents
Key Highlights of NCERT Solution for Class 10 Mathematics Chapter -2 Polynomials
Definition of Polynomial: An expression involving variables raised to whole number powers, with coefficients (e.g., P(x)=axn+bxn−1+…P(x) = ax^n + bx^{n-1} + \dots).
Types of Polynomials:
Monomial (one term)
Binomial (two terms)
Trinomial (three terms)
Degree of a Polynomial: The highest power of the variable in the polynomial.
Zeroes of a Polynomial: Values of xx that make the polynomial equal to zero.
Factorization of Polynomials: Expressing polynomials as a product of factors using methods like common factors, algebraic identities, and splitting the middle term.
Remainder Theorem: The remainder when dividing a polynomial P(x)P(x) by (x−a)(x – a) is P(a)P(a).
Factor Theorem: If P(a)=0P(a) = 0, then (x−a)(x – a) is a factor of P(x)P(x).
Important Identities: Basic algebraic identities for simplifying and factoring polynomials (e.g., (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2).
These are the key concepts that form the foundation of polynomials in Class 10.
Â
Â
Access NCERT Solutions for Mathematics Chapter 2- Polynomials
Exercise 2.1
Question 1: The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
Answer:
(i) The number of zeroes is 0 as the graph does not cut the x-axis at any point.
(ii) The number of zeroes is 1 as the graph intersects the x-axis at only 1 point.
(iii) The number of zeroes is 3 as the graph intersects the x-axis at 3 points.
(iv) The number of zeroes is 2 as the graph intersects the x-axis at 2 points.
(v) The number of zeroes is 4 as the graph intersects the x-axis at 4 points.
(vi) The number of zeroes is 3 as the graph intersects the x-axis at 3 points.
Exercise 2.2
Question 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
Answer:
Exercise 2.3
Question 1: Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
Question 2: Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
Question 3:
Question 4: On dividing 
by a polynomial g(x), the quotient and remainder were x − 2 and − 2x + 4, respectively. Find g(x).
Question 5: Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
Answer:
According to the division algorithm, if p(x) and g(x) are two polynomials with
g(x) ≠0, then we can find polynomials q(x) and r(x) such that
p(x) = g(x) × q(x) + r(x),
where r(x) = 0 or degree of r(x) < degree of g(x)
Degree of a polynomial is the highest power of the variable in the polynomial.
(i) deg p(x) = deg q(x)
Degree of quotient will be equal to degree of dividend when divisor is constant ( i.e., when any polynomial is divided by a constant).
Let us assume the division of 
by 2.
Thus, the division algorithm is satisfied.
(ii) deg q(x) = deg r(x)
Let us assume the division of x3 + x by x2,
Here, p(x) = x3 + x g(x) = x2
q(x) = x and r(x) = x
Clearly, the degree of q(x) and r(x) is the same i.e., 1. Checking for division algorithm,
p(x) = g(x) × q(x) + r(x) x3 + x = (x2 ) × x + x
x3 + x = x3 + x
Thus, the division algorithm is satisfied. (iii)deg r(x) = 0
Degree of remainder will be 0 when remainder comes to a constant. Let us assume the division of x3 + 1by x2.
Here, p(x) = x3 + 1
g(x) = x2
q(x) = x and r(x) = 1
Clearly, the degree of r(x) is 0. Checking for division algorithm, p(x) = g(x) × q(x) + r(x)
x3 + 1 = (x2 ) × x + 1
x3 + 1 = x3 + 1
Thus, the division algorithm is satisfied.
Exercise 2.4
Question 1: Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:
Therefore, 
, 1, and −2 are the zeroes of the given polynomial. Comparing the given polynomial with 
we obtain a = 2, b = 1, c = −5, d = 2
Therefore, the relationship between the zeroes and the coefficients is verified.
Therefore, 2, 1, 1 are the zeroes of the given polynomial.
Comparing the given polynomial with 
, we obtain a = 1, b = −4, c = 5, d = −2.
Verification of the relationship between zeroes and coefficient of the given polynomial
Multiplication of zeroes taking two at a time = (2)(1) + (1)(1) + (2)(1)
=2 + 1 + 2 = 5 
Hence, the relationship between the zeroes and the coefficients is verified.
Question 2: Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively.
Answer:
For finding the remaining zeroes of the given polynomial, we will find the quotient by dividing 
by x2 − 4x + 1.
It can be observed that 
is also a factor of the given polynomial.
Question 5: If the polynomial 
is divided by another polynomial 
, the remainder comes out to be x + a, find k and a.
Answer:
By division algorithm,
Dividend = Divisor × Quotient + Remainder
Dividend − Remainder = Divisor × Quotient
