Constant

From AoPSWiki

Revision as of 23:39, 30 January 2007 by JBL (Talk | contribs)

(diff) ← Older revision | Current revision (diff) | Newer revision → (diff)

Definition

A constant is a number with fixed value, unlike a variable that can change or that is used to represent an unknown value.

The word constant is also used in other contexts or as part of other expressions:

Constant function

A constant function is a function which has a constant output: the value of the function does not depend on the value of its input. Equivalently, a constant function is a function whose range has only a single value.

Constant term of a polynomial

The constant term of a polynomial in variables $x_1, x_2, \ldots, x_n$ is the coefficient of $x_1^0\cdot x_2^0 \cdots x_n^0$ . In the case of a polynomial in a single variable $x$ , it is the coefficient of the term $x_0^0$ . Normally, when we write out a polynomial, the constant term is the term with no variables present, e.g. for the polynomial $f(x) = x^3 + 2x^2 - 3x - 7$ , the constant term is $-7$ .