Answer
$x=-1$ or $x=1$
Work Step by Step
We solve by factoring with grouping:
$x^{3}+x^{2}-x-1=0$
$x^{2}(x+1)-1(x+1)=0$
$(x+1)(x^{2}-1)=0$
$(x+1)(x-1)(x+1)=0$
$x+1=0$ or $x-1=0$ or $x+1=0$
$x=-1$ or $x=1$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.