Consider the following screen shot & see the cubic polynomial in that there is function & table of it's forward difference
I read that a polynomial of degree "n" will have "n+1" difference as zero.But here in this case of cubic polynomial how can I find & prove 4th forward difference to be zero as in 3rd difference only one term is given.(this is the question I received)
Continue to evaluate $f(x)$ at $x=4$ and you shall get \begin{align}&f(x=4)=41\\&\Delta f(x)=31\\&\Delta ^2f(x)=22\\& \Delta ^3f(x)=12\\ \end{align} then you will get $\Delta ^4f(x)=0$.