Differences of Polynomials

Consider a polynomial of degree zero. If this is evaluated at integer values we get a sequence of values all the same, and the difference sequence is all zeroes. We say that the differencing operator S annihilates polynomials of degree zero. 

If the polynomial is of degree 1, then the values in the sequence vary linearly, and the first differences are all the same. These are in turn annihilated by the application of a second differencing operator. Thus 52 annihilates polynomials of degree 1. 

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