Suppose the polynomial f(x) is of degree 3 and satisfies f(3) = 2, f(4) = 4, f(5) = -2, and f(6) = 8. Determine the value of f(0).
+128460 We have the folllowing system
a3^3 + b 3^2 + c3 + d = 2
a4^3 + b4^2 + c4 + d = 4
a5^3 + b5^2 + c5 + d = -2
a6^3 + b6^2 + c6 + d = 8 simplify
27a + 9b + 3c + d = 2
64a + 16b + 4c + d = 4
125a + 25b + 5c + d = -2
216a + 36b + 6c + d = 8
This is a little lengthy to solve (but not impossible)...so....I will use a CAS to solve
a = 4 b = -52 c = 218 d = -292
f(0) = d = -292
