ALPHA DIVISION

Question 115

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Question

Let

\Delta

be an operator such that

\Delta(f(x))=f(x+1)-f(x)

. Furthermore,

\Delta^1(f(x))=\Delta(f(x))

and for

n\geq 2, \Delta^n(f(x))=\Delta(\Delta^{n-1}(f(x)))

. Given that f(x) is a polynomial and

\Delta^k(f(x))=c

, where c is a non-zero constant, find the degree of f(x).

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