x3-343
(x2 - xy + y2)(x + y)
x3 + x2 - 3x - 3 x(x2 + x - 3) - 3
If that's 2x2, the answer is (x + 2)(x2 + 4)
Since x3 is a factor of x5, it is automatically the GCF.
x3-343
(x - 7)(x2 + 7x + 49)
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x3 + 4x2 + x + 4 = (x + 4)(x2 + 1)
x3+27y3 = (x+3y) · (x2-3xy+9y2)
x2(x3 + 1) is the best you can do there.
x(x^2 + 2)
(x + 2)(x^2+4)
(x + 1)(x2 - x + 1)
(x2 - xy + y2)(x + y)
x3 + 8 = x3 + 23 = (x + 2)[x2 - (x)(2) + 22] = (x + 2) (x2 - 2x + 4)
x3 + 8 = x3 + 23 = (x + 2)(x2 + 2x + 22) = (x + 2)(x2 + 2x + 4)