Proof for chapter 27, A2c

[wecing]

Even though p(x) = pi^3 * x - pi^6 + pi^3 is within Q(pi^3)[x], p(pi^2 - 1) is actually pi^3 * (pi^2 - 1) - pi^6 + pi^3 = pi^5 - pi^6, which is not 0.

I think a better p(x) would be (x+1)^3 - (pi^3)^2 = x^3 + 3x^2 + 3x + 1 - (pi^3)^2. This is okay since 1, 3, and 1 - (pi^3)^2 are all within Q(pi^3) (e.g. 1 = (pi^3)^0 + 1).