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When a function is not a polynomial?

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Question: Identify if f(x) = 4 - 2/x^6 is a polynomial and if yes state its degree
when the exponents of the variable are non-negative and integer, the function is polynomial, else not.
whats the exponent of 'x' ?

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Other answers:

Not to mention, \(\sin(x)\) is not a polynomial either, even if it has a positive exponent.
its 6
why so parthkohli?
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 ?
-6 so its not a polynomial I guess :X
What about the sin(x) ?
yeah, its not, neither sin x
f(x) = sin(x)
What if the f(x) is a polynomial?
sin(x) = x3-x if I am not mistaken, *confused*
x^3 **
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 ...
hmm what sin(x) is equal to?
I am doing sin(x) and cos(x) atm they are pretty fresh into my mind :D
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.
cos x = 1-x^2/2!+x^4/4!-x^6/6!+....infinite terms
wait wait what is the notation of "!" used for here?
n! is read as n factorial and is defined as n*(n-1)*(n-2)*...3.2.1 example, 4! = 4*3*2*1
thank very much I understand now <3 !
so you see, sin x and cos x have infinite terms, hence not a polynomial. oh, Welcome ^_^

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