What is Polynomial Class 10?

Polynomials in Class 10 mathematics refer to a crucial algebraic concept where you learn about expressions consisting of variables, constants, and exponents, combined through addition, subtraction, and multiplication. It focuses on understanding and solving problems related to polynomial functions, especially quadratic polynomials.

In Class 10, the study of polynomials typically involves the following aspects:

• Definition and Types of Polynomials: Understanding what constitutes a polynomial and differentiating between various types based on their degree (linear, quadratic, cubic, etc.). For example, x + 2 is a linear polynomial, and x² + 3x + 2 is a quadratic polynomial.

• Zeroes of a Polynomial: Finding the values of the variable for which the polynomial equals zero. These zeroes are also known as the roots of the polynomial equation.

• Relationship between Zeroes and Coefficients: Exploring the relationship between the zeroes (roots) of a polynomial and its coefficients. For a quadratic polynomial ax² + bx + c, the sum of the zeroes is -b/a and the product of the zeroes is c/a.

• Division Algorithm for Polynomials: Applying the division algorithm to divide one polynomial by another, finding the quotient and remainder. This is expressed as: Dividend = (Divisor × Quotient) + Remainder.

• Quadratic Polynomials in Detail: Specifically focusing on quadratic polynomials, understanding how to find their zeroes using methods like factorization (splitting the middle term) and the quadratic formula.

• Examples:

  • Finding the zeroes of x² - 3x - 4. (The zeroes are x = 4 and x = -1).
  • Dividing x³ - 3x² + 5x - 3 by x - 2.

In summary, "Polynomial Class 10" encompasses a focused study on polynomials, emphasizing quadratic polynomials and their properties, including zeroes, relationships between zeroes and coefficients, and polynomial division. This knowledge is fundamental for further studies in algebra and calculus.