Constant term - wikipedia Constant term This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. ( December 2009 ) In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or can not change, because it does not contain any modifiable variables. For example, in the quadratic polynomial x 2 + 2 x + 3, ( displaystyle x ^ ( 2 ) + 2x + 3, ) 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 a x 2 + b x + c, ( displaystyle ax ^ ( 2 ) + bx + c, ) 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 ( x + 1 ) ( x − 2 ) ( displaystyle ( x + 1 ) ( x-2 ) ) 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 x. 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 x 2 + 2 x y + y 2 − 2 x + 2 y − 4 ( displaystyle x ^ ( 2 ) + 2xy + y ^ ( 2 ) - 2x + 2y - 4 ) has a constant term of − 4, which can be considered to be the coefficient of x y, where the variables are eliminated by being exponentiated to 0 ( any number exponentiated to 0 becomes 1 ). For any polynomial, the constant term can be obtained by substituting in 0 instead of each variable ; thus, eliminating each variable. The concept of exponentiation to 0 can be extended to power series and other types of series, for example in this power series : a 0 + a 1 x + a 2 x 2 + a 3 x 3 + ⋯, ( displaystyle a_ ( 0 ) + a_ ( 1 ) x + a_ ( 2 ) x ^ ( 2 ) + a_ ( 3 ) x ^ ( 3 ) + cdots, ) a is the constant term. In general a constant term is one that does not involve any variables at all. However in expressions that involve terms with other types of factors than constants and powers of variables, the notion of constant term can not be used in this sense, since that would lead to calling `` 4 '' the constant term of ( x − 3 ) 2 + 4 ( displaystyle ( x-3 ) ^ ( 2 ) + 4 ), whereas substituting 0 for x in this polynomial makes it evaluate to 13. See also Constant ( mathematics ) Retrieved from `` https://en.wikipedia.org/w/index.php?title=Constant_term&oldid=793633081 '' Categories : Polynomials Elementary algebra Hidden categories : Articles lacking sources from December 2009 All articles lacking sources Talk About Wikipedia فارسی Français 한국어 Edit links This page was last edited on 3 August 2017, at 00 : 39. About Wikipedia

Question: what does the constant term in the numerator represent
Answer: a term in an algebraic expression that has a value that is constant or cannot change