Question

How do you solve `(a-2)(a+4)>0`?

Answer 1

The answer is `x in ] -oo,-4 [ uu ] 2,+oo [`

Explanation:

Let `f(a)=(a-2)(a+4)`

Then we do a sign chart

`color(white)(aaaa)` `a` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-4` `color(white)(aaaa)` `2` `color(white)(aaaa)` `+oo`

`color(white)(aaaa)` `a+4` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `a-2` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `f(a)` `color(white)(aaaaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

For `f(a)>0`, `x in ] -oo,-4 [ uu ] 2,+oo [`