When you are given a polynomial and a binomial, you could determine if the binomial is a factor of the polynomial through the factor and remainder theorem. This is done by equation the binomial to zero. Then, substitute the value of x to the polynomial. If the answer is zero, then it is a factor. If not, then it has a remainder which is equivalent to whatever is the answer.
x - 1 = 0
x = 1
x^3 - 1
(1)^3 - 1 = 0
Therefore, (x-1) is a factor of x^3 - 1. The answer is C.
