Question

Lcm of x cubed-x squared+ x-1 and x squared -1

Answer 1

x^3 -x^2 + x -1

Factor by grouping

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

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

For the second one
x^2 -1 factors to (x-1)(x+1)


The LCM (x^2 +1)(x-1)(x+1)

Answer 2

x^3-x^2+x-1 = (x^2+1)(x-1)
x^2-1 = (x+1)(x-1)

So, the LCM is
(x^2+1)(x-1)(x+1)
= (x^2+1)(x^2-1)
= x^4-1