CBSE · Class 10 · Mathematics · PolynomialsDefine a polynomial and its degree. Also, explain the various types of polynomials. Use suitable examples to support your answer.

Definition of a Polynomial \nA polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The variables are raised to non-negative integer powers. For example, 2x^2 + 3x - 4 and x^3 - 2x^2 + x - 1 are polynomials.

Degree of a Polynomial\nThe degree of a polynomial is the highest power of the variable in the polynomial. For example, the degree of 2x^2 + 3x - 4 is 2, and the degree of x^3 - 2x^2 + x - 1 is 3.

Types of Polynomials

1. Monomial: A polynomial with only one term is called a monomial. For example, 3x^2 and 2y are monomials.
2. Binomial: A polynomial with two terms is called a binomial. For example, 2x^2 + 3x and x^2 - 2x + 1 are binomials.
3. Trinomial: A polynomial with three terms is called a trinomial. For example, 2x^2 + 3x - 4 and x^3 - 2x^2 + x - 1 are trinomials.
4. Quadratic Polynomial: A polynomial of degree two is called a quadratic polynomial. For example, 2x^2 + 3x - 4 and x^2 - 2x + 1 are quadratic polynomials.
5. Cubic Polynomial: A polynomial of degree three is called a cubic polynomial. For example, x^3 - 2x^2 + x - 1 and 2x^3 + 3x^2 - 4x + 1 are cubic polynomials.
6. Quartic Polynomial: A polynomial of degree four is called a quartic polynomial. For example, x^4 - 2x^3 + x^2 - 2x + 1 and 2x^4 + 3x^3 - 4x^2 + x + 1 are quartic polynomials.

Examples \nLet's consider the polynomial 2x^2 + 3x - 4. This polynomial is a quadratic polynomial because its degree is two. It is also a trinomial because it has three terms.