Choose the lowest of the exponents. The GCF of x3 and x5 is x3
x2(x - 8)
In the case of a binomial in general, the only way you can factor it is by looking for common factors in each term. In other words, check whether there is a common factor (in this case) in "6x" and in "27". If there is, take this factor out.
(x+2)(x2+2x+4)
(x - 6)(x2 + 6x + 36)
x3-343
(x + 7)(x2 - 7x + 49)
(x - 2)(x^2 + 2x + 4)
x5-1 = (x - 1)(x4 + x3 + x2 + 1)
(x - 1)(x4 + x3 + x2 + x + 1)
(x2 plus 40) (x minus 1)
x6 - y6 = (x3)2 - (y3)2 = (x3 + y3) (x3 - y3) = (x + y)(x2 - xy + y2)(x - y)(x2 + xy + y2)
10 is a root of x3 - 1000 = 0, so (x-10) is a factor. Use long division (x3 - 1000)/(x-10) to find x2 + 10x + 100, as the other factor.
x3-x2
x3 - 4x = x(x2 - 4) = x(x + 2)(x - 2)
x3 + 4x2 - 16x - 64 = (x + 4)(x + 4)(x - 4).
The only common factor of those two terms is the number three, giving you: 3(x3 - 8y3)