Suppose is a polynomial of degree five for which g(1) = 2, g(2) = 3, g(3) = 4, g(4) = 5, g(5) = 6, and g(6) = -113. Find g(0).

Guest Jan 12, 2019

#1**+2 **

We have this sytem of 6 equations

a + b + c + d + e + f = 2,

32a + 16b + 8c + 4d + 2e + f = 3,

243a + 81b + 27c + 9d + 3e + f = 4,

1024a + 256b + 64c + 16d + 4e + f = 5,

3125a + 625b + 125c + 25d + 5e + f = 6,

7776a + 1296b + 216c + 36d + 6e + f = -113

This system is* very* tedious to solve by hand [ so...I won't ]

We are only interested in the value of "f" because this will be the y intercept for g(0)

Using a matrix calculator......f is shown to be 121 = g(0)

CPhill Jan 12, 2019