A polynomial equation is a mathematical expression that involves variables raised to whole number powers, combined using addition, subtraction, and multiplication. The general form of a polynomial equation in one variable is a_n x^n + a_n-1 x^n-1 + ... + a_1 x + a_0 = 0 , where a_n, a_n-1, ..., a_0 are constants, and n is a non-negative integer representing the degree of the polynomial. Polynomial equations can have various degrees, such as linear (degree 1), quadratic (degree 2), or cubic (degree 3). They are fundamental in algebra and are used in various fields, including physics, engineering, and economics, to model relationships and solve problems. The solutions to polynomial equations are called roots, which can be found using different methods, such as factoring or the quadratic formula.