Question

Which of the following best describes the relationship between the binomial (x - 1) and the polynomial x3 - 1?

A. (x - 1) cannot be a factor because x3 - 1 is not quadratic.
B. (x - 1) is not a factor.
C. (x - 1) is a factor.
D. It is impossible to tell if (x - 1) is a factor.

Answer 1

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.