Hi Melody.
Here's the difference table that you asked to see.
\(\displaystyle \begin{array}{ccccccc}x&f(x)&\Delta &\Delta^{2} &\Delta^{3} &\Delta^{4} &\Delta^{5} \\ 1 & 2 &&&&&&\\ &&1 &&&&\\ 2&3 &&0&&&\\ &&1&&0&&\\ 3&4&&0&&0&\\ &&1&&0&& -140 \\ 4&5 &&0&& -140 &\\ && 1 && -140 &&\\ 5&6 && -140 &&&\\ && -139 &&&&\\ 6& -133 &&&&&\\ \end{array}\)
The x = 1 and f(x) = 2 at the top of the first two columns are x0 and f(x0).
Running down diagonally from the 2 are the forward differences for f(x0). They are, 1, 0, 0, 0, -140.
The next diagonal 1, 0, 0, -140 running down from the 3 are the forward differences for f(x1) and so on.
Let me know if you need any more info.
Tiggsy.