x^5 + x + 1 = 0, x^3 - x^2 = ?

x^5 + x + 1 = 0, x^3 - x^2 = ? x^5 + x + 1 = (x^3 - x^2) (x^2 + x + 1) + x^2 + x + 1 = (x^3 - x^2 + 1)(x^2 + x + 1) = 0 x^2 + x + 1 = x^2 + 2 * 1/2 * X + 1/2^2 + 3/4 >= 3/4 x^3 - x^2 + 1 = 0 x^3 - x^2 = -1