Polynomials: Is | 5x | a polynomial?

[SarahLee1233]

My math teacher isn't my favorite teacher. In my opinion, hhe's more of a read-from-the-book type of lady. Anyway, now I'm having trouble with polynomials.

I know that an expression containing a variable in a square root isn't a polynomial, and when the variable is in the demoninator it's not a polynomial. But if the expression is "l5xl" (that is, the absolute value of 5x), is it a polynomial? :?

 

[stapel]

My understanding would be that this is not a polynomial, in part due to the technical definition of "absolute value" (which involves square roots), and in part because another way of expressing absolute values is to use piecewise functions.

Eliz.

 

[tkhunny]

Your book should have a clear definition.

I like the highy-technical, braniac definition: If anything weird is going on with the variable, it's NOT a polynomial.

Watch out for unusual coefficients. They shouldn't bother you.

\(\displaystyle (\pi)x^{3}\;+\;[ln(3)]x^{2}\;+\;(\sqrt{2})x\;+\;(\gamma)\)

It's not pretty, but the coefficients shouldn't make any difference in your classification as polynomial or not a polynomial. It's still a polynomial.

 

[pka]

This may be far and away too technical an answer.
Every polynomial can be written in the following form:
\(\displaystyle \sum\limits_{k = 0}^n {a_k x^k } = a_0 + a_1 x + a_2 x^2 + \cdots + a_n x^n ,\quad a_k \in \Re.\)
In particular, each exponent is a non-negative integer and each coefficient is a real number (in some cases complex). If we cannot put an expression in that form then it is not a polynomial.