I'm trying to find the fifth difference (f(x+1) - f(x)) of a regular polynomial f(x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+ex+f but I keep messing up, help please!

Printable View

- Nov 12th 2012, 06:36 PMfraniosDifferences
I'm trying to find the fifth difference (f(x+1) - f(x)) of a regular polynomial f(x)=ax

^{5}+bx^{4}+cx^{3}+dx^{2}+ex+f but I keep messing up, help please! - Nov 12th 2012, 06:53 PMMarkFLRe: Differences
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.

- Nov 13th 2012, 07:21 AMfraniosRe: Differences
I tried, but i keep messing up when I get the fifth difference. The equation Im trying to find wont correspond.

- Nov 13th 2012, 11:30 AMMarkFLRe: Differences
When I compute the differences I suggested above, the pattern that emerges suggest the

*n*th difference of an*n*degree polynomial will be $\displaystyle n!a_n$. Proofs of this can be found online.