Answer
(negative infinity, $-4)$ U $(2$, infinity)
Work Step by Step
$(x-2)(x+4)>0$
$(x-2)=0$
$x=2$
$x+4=0$
$x=-4$
We have three ranges (where we need a point from each range):
(negative infinity, $-4)$
$(-4, 2)$
$(2$, infinity)
Let $x=-10$, $x=0$, and $x=10$
$x=-10$
$(x-2)(x+4)>0$
$(-10-2)(-10+4)>0$
$(-12)(-6)>0$
$72 > 0$ (true)
$x=0$
$(x-2)(x+4)>0$
$(0-2)(0+4)>0$
$(-2)(4)>0$
$-8>0$ (false)
$x=10$
$(x-2)(x+4)>0$
$(10-2)(10+4)>0$
$8*14>0$
$112 > 0$ (true)
(negative infinity, $-4)$ (true)
$(-4, 2)$ (false)
$(2$, infinity) (true)
