Differences

• November 12th 2012, 06:36 PM
franios
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!
• November 12th 2012, 06:53 PM
MarkFL
Re: 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.
• November 13th 2012, 07:21 AM
franios
Re: Differences
I tried, but i keep messing up when I get the fifth difference. The equation Im trying to find wont correspond.
• November 13th 2012, 11:30 AM
MarkFL
Re: Differences
When I compute the differences I suggested above, the pattern that emerges suggest the nth difference of an n degree polynomial will be $n!a_n$. Proofs of this can be found online.