premise: A polynomial is an expression and it is important in mathematics.
hypothesis: In field theory , a branch of mathematics , a minimal polynomial is defined relative to a field extension E/F and an element of the extension field E . In mathematics , a polynomial is an expression consisting of variables ( or indeterminates ) and coefficients , that involves only the operations of addition , subtraction , multiplication , and non-negative integer exponents . Polynomials appear in a wide variety of areas of mathematics and science . In advanced mathematics , polynomials are used to construct polynomial rings and algebraic varieties , central concepts in algebra and algebraic geometry . In mathematics , especially in the field of abstract algebra , a polynomial ring or polynomial algebra is a ring ( which is also a commutative algebra ) formed from the set of polynomials in one or more indeterminates ( traditionally also called variables ) with coefficients in another ring , often a field .