Question

How do you solve `(x+5)^2(x-2)>0` using a sign chart?

Answer 1

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

Explanation:

Let `f(x)=(x+5)^2(x-2)`

The domain of `f(x)` is `RR`

`AA x in RR, (x+5)^2>0`

The sign chart is easy

`color(white)(aaaa)` `x` `color(white)(aaaaaa)` `-oo` `color(white)(aaaaaa)` `2` `color(white)(aaaaaa)` `+oo`

`color(white)(aaaaa)` `x-2` `color(white)(aaaaaa)` `-` `color(white)(aaaaaa)` `+`

`color(white)(aaaaa)` `f(x)` `color(white)(aaaaaaa)` `-` `color(white)(aaaaaa)` `+`

Therefore,

`f(x)<0` when `x in ] 2,+oo [`