Suppose g(x) is a polynomial of degree five for which g(1) = 2, g(2) = 4, g(3) = 8, g(4) = 16, g(5) = 32, and g(6) = 64. Find g(0)
The polynomial is 2^x, so g(0) = 1.
Tempting though it is to go with the pattern of 2^x, notice that this is not a polynomial of degree 5.
The fifth order polynomial is g(x) = (x^5)/60 - (x^4)/6 + 11(x^3)/12 - 11(x^2)/6 + 46x/15 resulting in g(0) = 0;
