Chapter A.6, Problem 89AYU

To determine

To solve: $x^3+x^2-x-1=0$

Answer to Problem 89AYU

$x=\pm 1$

Explanation of Solution

$x^3+x^2-x-1=0$

$x^2\left(x+1\right)-1\left(x+1\right)=0$

$\left(x+1\right)\left(x^2-1\right)=0$

$x+1=0, x^2-1=0$

$x=-1, x^2=1$

$x=-1, x=\pm 1$