A polynomial function is a mathematical expression that consists of variables raised to whole number powers and multiplied by coefficients. The general form of a polynomial function is f(x) = a_n x^n + a_n-1 x^n-1 + \ldots + a_1 x + a_0 , where a_n, a_n-1, \ldots, a_0 are constants, and n is a non-negative integer representing the degree of the polynomial. Polynomial functions can have various shapes depending on their degree. For example, a linear polynomial (degree 1) forms a straight line, while a quadratic polynomial (degree 2) creates a parabolic curve. These functions are widely used in mathematics and applied fields, such as physics and engineering, to model real-world situations.