Class 10 Mathematics Chapter 2 - Polynomials Summary

Class 10 Mathematics  Chapter 2 - Polynomials Summary

• Polynomials are a fundamental topic in algebra and mathematics, covering a wide range of concepts and applications.
• Polynomials are algebraic expressions consisting of variables, coefficients, and exponents.
• The general form of a polynomial is P(x)=a_nxⁿ + a_n—1x^n—1 + ….+a₁x + a₀, where n is a non-negative integer, and a_n is the leading coefficient.
• The degree of a polynomial is the highest exponent of the variable in the polynomial. It determines the overall behavior of the polynomial.
• Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
• A quadratic polynomial in x with real coefficients is of the form ax² + bx + c, where a, b, c are real numbers with a ≠ 0.
• Roots or zeros of a polynomial are the values of x that make the polynomial equal to zero. They can be found by factoring or solving polynomial equations.
• The zeroes of a polynomial P(x) are precisely the x-coordinates of the points, where the graph of y = P(x) intersects the x -axis.
• A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.
• Polynomials can be added and subtracted by combining like terms, i.e., terms with the same variable and exponent.
• Multiplying two polynomials involves distributing each term in one polynomial with every term in the other polynomial and then simplifying the result.
• Polynomial division can be performed using long division or synthetic division. It's essential for finding roots and factors of polynomials.
• Factoring is the process of expressing a polynomial as a product of simpler polynomials. It's important for solving equations and understanding the behavior of functions.
• The Factor Theorem and Remainder Theorem: These theorems provide methods for determining whether a given value is a root of a polynomial and for finding the remainder when dividing a polynomial by a linear factor.
• If α and β are the zeroes of the quadratic polynomial ax² + bx + c, then

• If α, β, γ are the zeroes of the cubic polynomial ax³ + bx² + cx + d, then