Solve `x^2-x-2> 0.`

Explanation

`x^(2)-x-2 gt 0`
or `(x-2)(x+1)gt 0`
Now `x^(2)-x-2 = 0impliesx= -1,2.`
On the number line (x-axis) mark x = -1 and x = 2.
Now when `x gt 2,x+1 gt 0` and `x-2 gt 0`
`implies (x+1)(x-2) gt 0`
when `-1 lt x lt 2, x+1 gt 0` but `x-2 lt 0`
`implies (x+1)(x-2) lt 0`
when `x lt -1, x+1 lt 0 ` and `x-2 lt 0`
`implies (x+1)(x-2) gt 0`
Hence, sign scheme of `x^(2)-x-2` is

From the figure , `x^(2)-x-2 gt 0, x in (- oo, -1) cup (2,oo).`