Newton's Divided Difference Question

1. Jul 13, 2008

This is a problem from the book section about Newton's Divided Differences, but I don't see how it really connects to the chapter other than that you draw out the triangle diagram.

1. The problem statement, all variables and given/known data
Define $P(x) = P(x+1)-P(x), where P is an unknown 4th degree polynomial and that$^2P(x) = $($P(x)) = $(P(x+1)-P(x)) =$P(x+1) - $P(x) = P(x+2) -2(P(x+1) +P(x)) Given$^2 P(0) = 0, $^3 P(0) = 6,$^4 P(0) = 24

Find $^2 P(10) 2. Relevant equations 3. The attempt at a solution I used a4x^4 + a3x^3 + a2x^2 + a1x +a0 = Pn(x) and plugging in the givens I got that: a4 = 1, a3 = -5, a2 = -8, but I wasn't able to get a1 and a0 because they cancel out each time. I am not sure if I need a1 and a0 to find$^2 P(10), or if there is another way to do it.

Thanks in advance for any help.

2. Jul 15, 2008