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In algebra, an expression consisting of numbers and variables grouped according to certain patterns.
Specifically, polynomials are sums of monomials of the form a x n , where a (the coefficient) can be any real number and n (the degree) must be a whole number. A polynomial's degree is that of its monomial of highest degree. Like whole numbers, polynomials may be prime or factorable into products of primes. They may contain any number of variables , provided that the power of each variable is a nonnegative integer. They are the basis of algebraic equation solving. Setting a polynomial equal to zero results in a polynomial equation ; equating it to a variable results in a polynomial function , a particularly useful tool in modeling physical situations. Polynomial equations and functions can be analyzed completely by methods of algebra and calculus . See also orthoganal polynomial .