Question

how do you simplify polynomials?

Answer 1

what do you mean by simplify?

Answer 2

- First, try to factor binomial if possible (you can "make" a binomial without much effort up to degree 3)
- Then, it is posible to use general method to lower the degree like Bézout's method (up to degree 3), tschirnaus' method or Descartes method (up to degree 4), if that what you want to do.
- The method to choose depends upon the equation
- Computer symbolic algebra system can in almost all case do better than a human (like the FullSimplify[] function in Mathematica). Using it, and then find the path back to the original polynomial can give strong insight on how to simplify it efficiently.