Polynomial Theory is a branch of mathematics that studies polynomials, which are expressions made up of variables and coefficients combined using addition, subtraction, multiplication, and non-negative integer exponents. A polynomial can be represented in the form P(x) = a_n x^n + a_n-1 x^n-1 + ... + a_1 x + a_0 , where a_n, a_n-1, ..., a_0 are constants and n is a non-negative integer indicating the degree of the polynomial. The theory explores various properties of polynomials, including their roots, factors, and behavior under different operations. Important concepts include the Fundamental Theorem of Algebra, which states that every non-constant polynomial has at least one complex root, and polynomial long division, a method for dividing polynomials similar to numerical long division.