A coefficient in mathematics is a number or constant factor that multiplies a variable within a term of an algebraic expression or polynomial. It represents the magnitude by which the variable is scaled. For example, in the expression 3x3x3x, the coefficient of xxx is 3, and if a variable appears without an explicit number, its coefficient is assumed to be 1, as in x2x^2x2 where the coefficient is 1
. Coefficients can be positive or negative, whole numbers, fractions, decimals, or even imaginary numbers. They may also be symbols or letters representing constants in an expression, such as aaa and bbb in ax2+bx+cax^2+bx+cax2+bx+c, where aaa and bbb are coefficients of the variables x2x^2x2 and xxx, respectively
. The coefficient attached to the highest degree term in a polynomial is called the leading coefficient. Constant terms in an expression, which do not multiply any variable, are sometimes called constant coefficients or simply constants
. In summary, a coefficient is the multiplicative factor of a variable in a term, indicating how much the variable is multiplied by in an algebraic expression.
