Answer
(-infinity, $-2)$ U $(-2, 2)$
Work Step by Step
$x^3+2x^2-4x-8 <0$
$x^2(x+2)-4(x+2)<0$
$(x+2)(x^2-4)<0$
$(x+2)(x+2)(x-2)<0$
$(x+2)(x+2)(x-2)=0$
$x+2=0$
$x=-2$
$x-2=0$
$x=2$
(-infinity, $-2)$
$(-2, 2)$
$(2$, infinity)
Let $x=-10$, $x=0$, $x=10$
$x=-10$
$(x+2)(x+2)(x-2)<0$
$(-10+2)(-10+2)(-10-2)<0$
$-8*-8*-12<0$
$-768 < 0$ (true)
$x=0$
$(x+2)(x+2)(x-2)<0$
$(0+2)(0+2)(0-2)<0$
$2*2*-2 <0$
$-8< 0$ (true)
$x=10$
$(x+2)(x+2)(x-2)<0$
$(10+2)(10+2)(10-2)<0$
$12*12*8 < 0$
$1152 <0$ (false)
