COEFFICIENT, a term used in algebra originally to repre sent either of the two rational factors of a monomial. For example, in its primitive meaning, in the expression ab either a or b would be the coefficient of the other, the two acting together with the same efficiency. The meaning of the word has, however, been gradually enlarged as algebra has developed. At present a co efficient is generally considered as a number or other known factor written before an algebraic expression. For example, in the expression 2a is the coefficient of but 2 is also con sidered as the coefficient of axe. Similarly, in the case of ixy, the coefficient of xy is 1, and in the expression la 1/3 a V3 is the coefficient of x— y. The term was introduced into algebra by Vieta (Viete), at the close of the 16th century. In algebra it is often required to perform some such operation as the division of — — 2 2x+ 3 by This is conveniently done by using detached coefficients, simply dividing 1-7+19-22+3 by 1-3, using the ordinary arrangement of work, or that of synthetic division as explained in textbooks. This saves the labour of frequently writing the letters during the operation. (See ALGEBRA;