Constant term
In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomial
the 3 is a constant term.
After like terms are combined, an algebraic expression will have at most one constant term. Thus, it is common to speak of the quadratic polynomial
where x is the variable, and has a constant term of c. If c = 0, then the constant term will not actually appear when the quadratic is written.
It is notable that a term that is constant, with a constant as a multiplicative coefficient added to it (although this expression could be more simply written as their product), still constitutes a constant term as a variable is still not present in the new term. Although the expression is modified, the term (and coefficient) itself classifies as constant. However, should this introduced coefficient contain a variable, while the original number has a constant meaning, this has no bearing if the new term stays constant as the introduced coefficient will always override the constant expression - for example, in when x is multiplied by 2, the result, 2x, is not constant; while 1 * -2 is -2 and still a constant.
Any polynomial written in standard form has a unique constant term, which can be considered a coefficient of x0. In particular, the constant term will always be the lowest degree term of the polynomial. This also applies to multivariate polynomials. For example, the polynomial
...
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