(x^3 - 1)
= (x - 1)[x^2 + (x)(1) + 1^2]
= (x - 1)(x^2 + x + 1)
The greatest common factor of 1-x3 is 1, dummy.
(x + 1)(x2 - x + 1)
(x - 1)(x2 + x - 1)
x3-343
x2(x3 + 1) is the best you can do there.
x3 + 2x2 + 5x + 4 = (x + 1)(x2 + x + 4)
Since x3 is a factor of x5, it is automatically the GCF.
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)
Greatest common factor of x4 and x3 is x3.