Thread: Differences

I'm trying to find the fifth difference (f(x+1) - f(x)) of a regular polynomial f(x)=ax⁵+bx⁴+cx³+dx²+ex+f but I keep messing up, help please!

Try finding the first difference of a linear function, the second difference of a quadratic, the third difference of a cubic, and you should see a pattern emerge.

I tried, but i keep messing up when I get the fifth difference. The equation Im trying to find wont correspond.

When I compute the differences I suggested above, the pattern that emerges suggest the nth difference of an n degree polynomial will be . Proofs of this can be found online.