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 $

Question

parthkohli · Answer

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

amistre64 · Answer

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)]\

amistre64 · Answer

$$no latex?$$hmmm

parthkohli · Answer

So this is a polynomial, right?

parthkohli · Answer

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

amistre64 · Answer

lol, accursed typos!!

amistre64 · Answer

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

parthkohli · Answer

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

amistre64 · Answer

the variables are pretty much accounted for by adding up the appropriate:(a+b)^n parts, n=0,1,2,3,....

amistre64 · Answer

yes

parthkohli · Answer

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

amistre64 · Answer

polynomials of a single variable is what id call them.

parthkohli · Answer

OK - that clears it up. Thanks!

amistre64 · Answer

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

amistre64 · Answer

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

parthkohli · Answer

That makes sense!