Polynomial equations

A polynomial equation is an equationin which a polynomial is set equal to another polynomial.

is a polynomial equation. In case of a polynomial equation the variable is considered an unknown, and one seeks to find the possible values for which both members of the equation evaluate to the same value (in general more than one solution may exist). A polynomial equation is to be contrasted with a polynomial identity like (x + y)(x – y) = x2–y2, where both members represent the same polynomial in different forms, and as a consequence any evaluation of both members will give a valid equality.