We see that the two terms share an x, so we can pull that out:
[tex]x^3-x=x(x^2-1)[/tex]
Now notice that we have a difference of squares ([tex]x^2-1[/tex]). Given a difference of squares, [tex]a^2-b^2[/tex], this can always be factored into [tex](a+b)(a-b)[/tex]. We can use this in this case: [tex]x^2-1=(x+1)(x-1)[/tex].
So, our final factorized form is: [tex]x(x+1)(x-1)[/tex].
