find the least common multiple of x^3 - x^2 + x - 1 and x^2 - 1. write the answer in factored form.
To find the least common multiple (LCM) of two polynomials, we need to first factorize them completely.
Factorizing x^3 - x^2 + x - 1:
x^3 - x^2 + x - 1 = (x - 1)(x^2 + 1)
Factorizing x^2 - 1:
x^2 - 1 = (x - 1)(x + 1)
Now, to find the LCM, we multiply the highest power of each factor that appears in the factorizations of both polynomials:
LCM = (x - 1)(x + 1)(x^2 + 1)
Thus, the LCM of x^3 - x^2 + x - 1 and x^2 - 1 is (x - 1)(x + 1)(x^2 + 1) in factored form.