Question

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)

Answer 1

It's B.

Answer 2

Factor first the \[x ^{3}-x ^{2}+x-1\]by grouping. Like this:

Answer 3

\[(x ^{3}-x ^{2})+(x-1)\]

Answer 4

Factor the first set of parenthesis like this:

Answer 5

\[x ^{2}(x-1)\]and you still have the + (x - 1), so actually what you have is this:

Answer 6

\[x ^{2}(x-1)+(x-1)\]You can factor that further by taking out an (x - 1), like this:

Answer 7

\[(x-1)[x ^{2}+1]\]

Answer 8

That's the factorization of the third degree polynomial. The other one goes like this, and much simpler:\[(x ^{2}-1)=(x+1)(x-1)\]

Answer 9

So you have (x+1)(x-1)(x^2+1). See?

Answer 10

Yeah thanks :)

Answer 11

You're welcome!