Question

Question 42 Unsaved

Find the least common multiple of x3 - x2 + x - 1 and x2 - 1. Write the answer in factored form.

Question 42 options:

(x3 - x2 + x - 1)(x2 - 1)


(x + 1)(x - 1)(x2 + 1)


(x + 1)(x - 1)(x2 - 1)


(x + 1)2(x - 1)

Answer 1

`x^3-x^2+x-1=x^2(x-1)+1(x-1)=\boxed{(x-1)}(x^2+1)\\\\x^2-1=x^2-1^2=\boxed{(x-1)}(x+1)\\\\LCM=\boxed{(x-1)}(x^2+1)(x+1)`

`Answer:\ (x+1)(x-1)(x^2+1)`