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On the other hand, it is a polynomial because it is filled with terms.

\[no latex?\]hmmm

So this is a polynomial, right?

I think you used ]\ instead of \] :-)

lol, accursed typos!!

yes, a+b is a polynomial of the form:
\[f(a.b)=c_0a+c_1b+c_2a^2+c_3b^2+c_4a^2b+c_5ab^2+...\]

Oh, I get where you are getting. The \(f(x)\) is just a specialized type of polynomial

yes

But what are the polynomials in the form \(a + bx + cx^2 \cdots\) called?

polynomials of a single variable is what id call them.

OK - that clears it up. Thanks!

http://www.wolframalpha.com/input/?i=polynomial
a poly in one var ....

That makes sense!