Question

When a function is not a polynomial?

Answer 1

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

Answer 2

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

Answer 3

whats the exponent of 'x' ?

Answer 4

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

Answer 5

its 6

Answer 6

why so parthkohli?

Answer 7

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 ?

Answer 8

-6 so its not a polynomial I guess :X

Answer 9

What about the sin(x) ?

Answer 10

yeah, its not, neither sin x

Answer 11

f(x) = sin(x)

Answer 12

What if the f(x) is a polynomial?

Answer 13

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

Answer 14

x^3 **

Answer 15

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 ...

Answer 16

hmm what sin(x) is equal to?

Answer 17

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

Answer 18

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.

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

oohhh

Answer 23

thank very much I understand now <3 !

Answer 24

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