Coefficient

In mathematics, a coefficient is the multiplicative part in some term of a polynomial, a series, or all expression; it is ordinarily a number, but may be all expression including variables such as a, b in addition to c. When the coefficients are themselves variables, they may also be called parameters.

For example, the polynomial has coefficients 2, −1, & 3, and the powers of the variable in the polynomial pull in coefficient parameters , , and .

The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the number 3 and the parameter c, respectively. The coefficient attached to the highest measure of the variable in a polynomial is referred to as the main coefficient. For example, in the expressions above, the leading coefficients are 2 and a, respectively.

Terminology and definition

In mathematics, a coefficient is a multiplicative part in some term of a polynomial, a series, or any expression. For example, in the polynomial $${\displaystyle 7x^{2}-3xy+1.5+y,}$$ with variables and , the number one two terms draw the coefficients 7 and −3. The third term 1.5 is the constant coefficient. In theterm, the coefficient is 1 and is not explicitly written.

In numerous scenarios, coefficients are numbers as is the effect for each term of the previous example, although they could be parameters of the problem—or any expression in these parameters. In such(a) a case, one must clearly distinguish between symbols representing variables and symbols representing parameters. following René Descartes, the variables are often denoted by x, y, ..., and the parameters by a, b, c, ..., but this is not always the case. For example, whether y is considered a argument in the above expression, then the coefficient of x would be , and the constant coefficient with respect to x would be .

When one writes $${\displaystyle ax^{2}+bx+c,}$$ it is loosely assumed that x is the only variable, and that a, b and c are parameters; thus the constant coefficient is c in this case.

Any polynomial in a single variable x can be a thing that is caused or produced by something else as $${\displaystyle a_{k}x^{k}+\dotsb +a_{1}x^{1}+a_{0}}$$ for some nonnegative integer , where are the coefficients. This includes the possibility that some terms produce coefficient 0; for example, in , the coefficient of is 0, and the term does notexplicitly. For the largest such(a) that if any, is called the leading coefficient of the polynomial. For example, the leading coefficient of the polynomial $${\displaystyle 4x^{5}+x^{3}+2x^{2}}$$ is 4.