Coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression. In the latter case, the variables appearing in the coefficients are often called parameters, and must be clearly distinguished from the other variables. The coefficients of an algebraic term can be positive or negative, and this multiplies the unknown term.
For example:
In 2a, 2 is the coefficient of a;
In x, 1 is the coefficient of x but it is not visible;
In 2/3p, 2/3 is the coefficient of p;
In -3f, -3 is the coefficient of f.
In 2t + t -f + 2f + 8, 3 is the coefficient of x and 1 the coefficient of y (2t + t = 3t, - f + 2f = f)
Variable is a symbol, commonly a single letter, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown. Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation. A typical example is the quadratic formula, which allows one to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation for the variables that represent them.
