Find the least common multiple of x 3 - x 2 + x - 1 and x 2 - 1. write the answer in factored form.a. (x + 1) 2(x - 1) b. (x + 1)(x - 1)(x 2 + 1) c. (x 3 - x 2 + x - 1)(x 2 - 1) d. (x + 1)(x - 1)(x 2 - 1)

Let
f(x) = x³ - x² + x - 1
g(x) = x² - 1

By the remainder theorem, f(1) = 1 -1 + 1 - 1 = 0
Therefore (x-1) is a factor.
Perform synthetic division.

1 | 1  -1   1  -1
         1  0   1
   --------------
    1   0  1   0

Therefore,
f(x) = (x-1)(x²+1)

Also,
g(x) = (x+1)(x-1)

Answer: b.
The least common multiple for f(x) and g(x) is (x + 1)(x - 1)(x² + 1).