Monomial
In mathematics, a
monomial is, roughly speaking, a polynomial which has only one term. Two different definitions of a monomial may be encountered: ▪ For the first definition, a
monomial is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. The constant 1 is a monomial, being equal to the empty product and x0 for any variable x. If only a single variable x is considered, this means that a monomial is either 1 or a power
xn of x, with n a positive integer. If several variables are considered, say,, , , then each can be given an exponent, so that any monomial is of the form with non-negative integers. ▪ For the second definition, a
monomial is a monomial in the first sense multiplied by a nonzero constant, called the
coefficient of the monomial. A monomial in the first sense is also a monomial in the second sense, because the multiplication by 1 is allowed. For example, in this interpretation and are monomials.