Question

Find the least common multiple of x3 - x2 + x - 1 and x2 - 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)

Answer 1

The solution to the problem is as follows:

x^3-x^2 +x -1= x^2(x-1) +(x-1)=(x-1)(x^2+1) ,(common factor x-1 

(x^2-1)=(x-1)(x+1) 

LCM=(x-1)(x^2+1)(x+1) 

=(x^2-1)(x^2+1)=x^4-1

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 2

The correct answer to your question is letter B. (x + 1)(x - 1)(x^2 + 1)