I'm not sure I understand what it means to "solve polynomials" (to simplify them, or what?). However:
Imagine that you need a smooth curve to connect some points. Why? For the beauty to it is not broken ) That point in the format (x,y): (0,0),(1,1),(2,0),(3,1), here is the solution
. This is one of an infinite number of solutions, among others it stands out because it is the minimum degree polynomial satisfying the condition. This is a very well - to multiply and stack the processor will be much faster than calculating, say, the sinuses, and therefore can very quickly calculate the height of the point on the curve for any X.