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I don't understand this: is \(a + b\) a polynomial? They say that a polynomial is filled with constant coefficients and a single variable, that is, a polynomial is in the form \(f(x) = a + bx + cx^2 \cdots \)

Mathematics
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On the other hand, it is a polynomial because it is filled with terms.
a poly of one variable is expressed as your f(x) a poly of multiple variables is defined for: \[f(x_1,x_2,...,x_n)]\
\[no latex?\]hmmm

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Other answers:

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
the variables are pretty much accounted for by adding up the appropriate:(a+b)^n parts, n=0,1,2,3,....
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 ....
think of a poly as a summation: \[f(x)=\sum_{n=0}^{N}(x)^n\] \[f(x,y)=\sum_{n=0}^{N}(x+y)^n\] \[f(x,y,z)=\sum_{n=0}^{N}(x+y+z)^n\] with something applied for constant coeefs
That makes sense!

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