Class 10 Maths | Chapter 2 - Polynomials | Lecture 1 - Introduction | GSEB English Medium 2026 - 27

Описание: Welcome to Chapter 2 – Polynomials (Lecture 1) of Class 10 Maths GSEB English Medium.
In this lecture, we begin the introduction to Polynomials and understand the basic concepts that are very important for board exams.
This video covers the following topics:
✔ Definition of Polynomial
✔ Types of Polynomials based on number of terms
 • Monomial
 • Binomial
 • Trinomial
✔ Degree of a Polynomial
✔ Zero Polynomial
✔ Types of Polynomials based on Degree
 • Constant Polynomial
 • Linear Polynomial
 • Quadratic Polynomial
 • Cubic Polynomial
✔ Zeroes of a Polynomial
✔ Maximum number of zeroes of a polynomial
These concepts are very important for GSEB Class 10 board exams and help in understanding upcoming topics of the chapter.
This lecture is part of the complete Class 10 Maths GSEB English Medium course for 2026–27 board exam preparation.
📚 Chapter: Polynomials
🎥 Lecture: 1
🏫 Board: GSEB
📖 Class: 10 Maths

Content :
--} Polynomials : An algebraic expression consisting of variables, coefficients, operations of Addition, Subtraction, multiplication and non - negative integers (Whole numbers) exponents.
--} Types of Polynomial based on number of terms :
Monomial, Binomial and Trinomial
--} In the following, _______ is not a polynomial in x. [March 2012]
(A) 4x^2 + root 7 (B) 3x^2 - x - 1 (C) 3x^2 - 5 root x + 2 (D) 3x - 2
--} From the following, ______ is not a polynomial in x. [March 2011]
(A) Root x - 5 (B) 3x^2 - root 5 (C) 3/2 x^2 - x - 2 (D) 5x^2 - x + 1
--} From the following, ______ is rational expression but not a polynomial. [March 2011]
(A) x - 5 / x - 3 (B) x^2 - 9 / x - 3 (C) x^3 - 8 / x^2 + 2x + 4 (D) x - 3 / 3 - x
--} Degree of the polynomial : The highest power of variable among all the terms of the polynomial is known as the degree of polynomial.
--} Zero polynomial : The coefficient of a polynomial is zero, then the polynomial is known as zero polynomial.
--} Degree of zero polynomial is not defined.
--} Zeroes of zero polynomial is any real number.
--} Types of polynomials based on degree :
Constant polynomial, Linear polynomial, Quadratic polynomial, Cubic polynomials and Bi - quadratic polynomials.
--} Root 3 x + 5 is a linear polynomial. [June 2022, March 2025]
--} The degree of polynomial (x + 1)(x^2 - x - x^4 + 1) is ________. [March 2015]
(A) 5 (B) 4 (C) 1 (D) 3
--} Zero(s) of a polynomial : The value(s) of a variable at which the value of a polynomial is zero.
--} Number of zeroes :
The maximum number of zeroes of a linear polynomial is 1.
The maximum number of zeroes of a Quadratic polynomial is 2.
The maximum number of zeroes of a Cubic polynomial is 3.
So, the maximum number of zeroes of a polynomial is equal to the degree of the polynomial.
--} Match the following : [March 2022]
The zero of P(x) = 2x - 6 is _________. (a) 0 (b) 1 (c) 3
--} Match the following : [March 2025]
P(x) = x^3 + x^2 and P(x) = x^3 - x (a) 1 (b) 2 (c) 3
--} The zero of the linear polynomial ax + b is -a/b. [March 2024]
--} If P(3) = 0, then (x - 3) is one of the factor of P(x). [March 2022]
--} If P(x) = x^2 - 7x + 10, then the number of zeroes is 3. [March 2023]
--} The quadratic polynomial P(x) = x^2 + x has 2 real zeroes. [June 2021]
--} Number of zeroes of polynomial P(x) = x^3 - x are 3. [March 2022, June 2023]
--} If one zero of the quadratic polynomial x^2 + 3x + k is 2, then the value of k is [NCERT Exemplar]
(A) 10 (B) -10 (C) 5 (D) -5
--} If one of the zeroes of the quadratic polynomial (k - 1)x^2 + kx + 1 is -3, then the value of k is
(A) 4/3 (B) -4/3 (C) 2/3 (D) -2/3
--} If the zeroes of the quadratic polynomial x^2 + (a + 1)x + b are 2 and -3, then [NCERT Exemplar]
(A) a = -7, b = -1 (B) a = 5, b = -1 (C) a = 2, b = -6 (D) a = 0, b = -6
--} The number of real zeroes of polynomial P(x) = x^3 - x is _____. [March 2015]
(A) 2 (B) 1 (C) 0 (D) 3
--} The cubic polynomial P(a) = a^3 - a has ______ zeroes. [March 2013]
(A) 0 (B) 1 (C) 2 (D) 3
--} Which of the following is not a zero of the polynomial P(x) = x^3 - x? [March 2019]
(A) 0 (B) 1 (C) -1 (D) 3