`  I can do a rewrite of the ``Overview`` section, but I will need to know the consensus on a few things first. As I understand it, the polynomial can be expressed in many ways, e.g., (x-1)(x+1)=x2-1. Are we only calling the fully expanded form a polynomial, or is every equivalent expression also a polynomial? Also, I think there should be several illustrative examples of what is and is not a polynomial very early in the article. Tell me what you think.`