LITERAL COEFFICIENT

The expression "4x" denotes a multiple of 'x'. The number 4, which indicates the multiple, is called the coefficient of 'x' or more specifically the numerical coefficient of 'x'. Can 'x' be called the coefficient of '4'?

The coefficient may be a constant number like 4, called a numerical coefficient , or a variable like 'x', called a literal coefficient

Thus in the expression 'nx', 'n' may be regarded as the coefficient of 'x'. But in some problems, when we are thinking of multiples of 'n', 'x' would be a coefficient of 'n'. In such a case, we would usually write the expression as "xn". Therefore, writing the coefficient first in the expression is a practice.

In general, if an expression is the product of several factors, any one of them can be regarded as the coefficient of the product of the others. Coefficients can also be a combination of literal and numerical as in the example below:
Ex: In the expression –27x2y,
      –27 is the numerical coefficient of x2y
      x2 is the literal coefficient of –27y
      y is the literal coefficient of –27x2
      –27x2 is the coefficient of y
      –27y is the coefficient of x2

Important note: Unless otherwise specified, coefficient means numerical coefficient only.