Definition of Polynomial

A polynomial is a mathematical expression that consists of variables (also known as indeterminates) and coefficients, combined using only the operations of addition, subtraction, and multiplication, and raised to non-negative integer powers.

It can be written in the form of:

a_n*x^n + a_(n-1)x^(n-1) + ... + a_1x + a_0

where n is the degree of the polynomial, x is the variable, a_n, a_(n-1), ..., a_1, a_0 are coefficients and a_n is non-zero.

For example, the polynomial 3x^2 + 2x - 5 is a polynomial of degree 2, with variable x, and coefficients 3, 2, and -5. The degree of a polynomial is defined as the highest power of the variable in the polynomial and is commonly represented by n.

It is also said that a polynomial is a sum of one or more monomials, where a monomial is a single term such as x^3, 5x^2, -3x, or 7.

In general, polynomials are used to model and describe various phenomena in physics, engineering, finance, and many other fields, and they can be used to solve a wide range of mathematical problems, including optimization, interpolation, and solving systems of equations.