## ParthKohli 2 years ago 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 $$f(x) = a + bx + cx^2 \cdots$$

1. ParthKohli

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

2. amistre64

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)]\ 3. amistre64 \[no latex?$hmmm

4. ParthKohli

So this is a polynomial, right?

5. ParthKohli

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

6. amistre64

lol, accursed typos!!

7. amistre64

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

8. ParthKohli

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

9. amistre64

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

10. amistre64

yes

11. ParthKohli

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

12. amistre64

polynomials of a single variable is what id call them.

13. ParthKohli

OK - that clears it up. Thanks!

14. amistre64

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

15. amistre64

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

16. ParthKohli

That makes sense!