A coefficient, in math, refers to the number that precedes a letter variable. For example, in the term 4*x, the coefficient is equal to 4, while the variable is "x." If a number is not attached to a variable through a multiplication operator, it is simply called a constant.
A coefficient is one of the main components of a monomial. A monomial is a single term composed of a coefficient and variable through a multiplication operation. Monomials can be added or subtracted to each other, which forms a polynomial statement or function. While a coefficient can be attached to a variable with a negative exponent, that term would not be considered a monomial, due to the negative exponent.