polynomials are generalizations of number. you use them to solve equations just like you use all numbers. polynomials add the notion of an "indeterminate" in t

polynomials are generalizations of number. you use them to solve equations just like you use all numbers. polynomials add the notion of an "indeterminate" in the same way that you use integers to solve equations like 3 + x = 2 (x = -1), or rationals to solve 3x = 2 (x = 2/3). you use polynomials to model equations like x^2 = x + 1 (x = phi). or to perform polynomial division. or to do algebraic geometry (x^2 + y^2 - 1 = 0 => unit circle)