In algebra, a term is a product of the form 
(in the univariate case), or more generally of the form
(in the multivariate
case) in a polynomial (Becker and Weispfenning 1993,
p. 188).
The word "term" is also used commonly to mean a summand of a polynomial including its coefficient (more properly called a monomial), or the corresponding quantity in a series (i.e., a series term).
One term is said to divide another if the powers of its variables are no greater than the corresponding powers in the second monomial. For example, 
divides 
but does not divide 
. A term 
is said to reduce with respect to a polynomial if the leading
term of that polynomial divides 
. For example, 
reduces with respect to 
because 
divides 
, and the result of this reduction is 
, or 
. A polynomial can therefore be reduced by reducing
its terms beginning with the greatest and proceeding downward. Similarly, a polynomial
can be reduced with respect to a set of polynomials by reducing in turn with respect
to each element in that set. A polynomial is fully reduced if none of its terms can
be reduced (Lichtblau 1996).
