(x + 1)(x2 - x + 1)
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x3 + 4x2 + x + 4 = (x + 4)(x2 + 1)
x2(x3 + 1) is the best you can do there.
(x - 1)(x2 + x - 1)
x3 - 3x2 + x - 3 = (x2 +1)( x - 3)
3 - 3x + x2 - x3 = (1 - x)(x2 + 3)
x3 - 3x2 + x - 3 = (x - 3)(x2 + 1)
x3 - 2x2 + x - 2 =(x - 2)(x2 + 1)
x(x - 13)(x - 1)
(x2 plus 40) (x minus 1)
The greatest common factor of 1-x3 is 1, dummy.
(x - 1)(x^2 - 5)