Only if your polynomial is written as a binomial, i.e. and is a positive integer.
The binomial expansion is , where .
So each coefficient of will be .
Say I have a regular polynomial like or .
Is there a way to extract the coefficient for the nth degree?
For example, if and I need the coefficient for (which is 5 in this case), is there some magic function g(f,n) which does:
g(f(x),2) = 5
?
(and similarly, g(f(x),3) would be 4, etc)
I see, thanks. So there's no trick to extract coefficients from any polynomial in general? (I was thinking maybe something smart with modulo or something, but didn't really get anywhere)
How about the specific case where the polynomial looks like ? Any clever possibilities there?