Step-by-step explanation:
[tex] - x {}^{3 } - {x}^{2} + x + 1[/tex]
[tex] - {x}^{2} ( x + 1) + 1(x + 1)[/tex]
[tex](1 - {x}^{2} )(x + 1) = 0[/tex]
[tex](1 - x)(1 + x)(x + 1) = 0[/tex]
[tex]1- x = 0[/tex]
[tex]x = 1[/tex]
[tex]1 + x = 0[/tex]
[tex]x = - 1[/tex]
[tex]x = - 1[/tex]
So we have the answer of
-1 and 1.
