If f(x) is a monic quartic polynomial such that f(-1)=-1, f(2)=-4, f(-3)=9, and f(4)=-16, find f(1).
+129847 We have the following form
x^4 + bx^3 + cx^2 + dx + e
We have this system
1 - b + c - d + e = -1
16 + 8b + 4c + 2d + e = -4
81 - 27b + 9c - 3d + e = 9
256 + 64b + 16c + 4d + e = -16 rearranging we have
-b + c - d + e = -2
8b + 4c + 2d + e = -20
-27b + 9c - 3d + e = -72
64b + 16c + 4d + e = -272
This is tedious to solve ( but not impossible) so I'm using some technology to find b,c,d and e
a = 1
b = -79/35
c = -89/7
d = 472/35
e = 768/35
f(1) is just the sum of these = 751 / 35
