## Christos 2 years ago When a function is not a polynomial?

1. Christos

Question: Identify if f(x) = 4 - 2/x^6 is a polynomial and if yes state its degree

2. hartnn

when the exponents of the variable are non-negative and integer, the function is polynomial, else not.

3. hartnn

whats the exponent of 'x' ?

4. ParthKohli

Not to mention, $$\sin(x)$$ is not a polynomial either, even if it has a positive exponent.

5. Christos

its 6

6. Christos

why so parthkohli?

7. hartnn

ofcourse, my definition is incomplete , but it suffices in this case. and the term is 2/x^6 which equals, 2x^{-6} now whats the exponent ?

8. Christos

-6 so its not a polynomial I guess :X

9. Christos

10. hartnn

yeah, its not, neither sin x

11. Christos

f(x) = sin(x)

12. Christos

What if the f(x) is a polynomial?

13. Christos

sin(x) = x3-x if I am not mistaken, *confused*

14. Christos

x^3 **

15. hartnn

for polynomial function, exponents of the variable are non-negative and integer example: 1-x^5+x^99 or x^2+x+1 and so on.. sin x is a function of 'x' and no, sin x is not x^3-x ...

16. Christos

hmm what sin(x) is equal to?

17. Christos

I am doing sin(x) and cos(x) atm they are pretty fresh into my mind :D

18. hartnn

sin x = x-x^3/3! +x^5/5!-x^7/7! ....infinite terms for function to be polynomial, the number of terms should be finite. this is the reason why sin x is not a polynomial.

19. hartnn

cos x = 1-x^2/2!+x^4/4!-x^6/6!+....infinite terms

20. Christos

wait wait what is the notation of "!" used for here?

21. hartnn

n! is read as n factorial and is defined as n*(n-1)*(n-2)*...3.2.1 example, 4! = 4*3*2*1

22. Christos

oohhh

23. Christos

thank very much I understand now <3 !

24. hartnn

so you see, sin x and cos x have infinite terms, hence not a polynomial. oh, Welcome ^_^