x^2 + 2x - 8 > 0

First let us facotor:

x^2 + 2x -8 = (x+4)(x-2) > 0

Then we have two cases:

In order for the function to be positive, then :

(x+4) > 0 AND (x-2) > 0

==> x > -4 and x > 2

==>** x belongs to (2,inf)...........(1)**

The second case is:

(x+4)< 0 AND (x-2) < 0

==> x < -4 and x < 2

==> **x belongs to (-inf, -4)...........(2)**

**==> from (1) and (2) we conclude that:**

**x belongs to (-inf, -4) U (2,inf).**

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