how to simply x^3 + x + 2 ?

As x3 + x + 2 is the simpliest form, I guess that you are asking about how to factorize x3 + x + 2.

Let f(x) = x3 + x + 2.

f(-1) = (-1)3 + (-1) + 2 = -1 - 1 + 2 = 0

By factor theorem, x + 1 is a factor of f(x).

f(x)
= x3 + x + 2
= x3 + x2 - x2 - x + 2x + 2
= x2(x - 1) - x(x + 1) + 2(x + 1)
= (x - 1)(x2 - x + 2)

2007-03-10 18:57:13 補充：
stephentavington, 你的long division做錯了.發問者請注意, 發問者自選是對答題者的尊重, 沒有尊重, 就沒有人會再在這裡答題.