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

Dec 28, 2016

The answer is x in ] 2,+oo [

#### Explanation:

Let $f \left(x\right) = {\left(x + 5\right)}^{2} \left(x - 2\right)$

The domain of $f \left(x\right)$ is $\mathbb{R}$

$\forall x \in \mathbb{R} , {\left(x + 5\right)}^{2} > 0$

The sign chart is easy

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a a a}$$2$$\textcolor{w h i t e}{a a a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a a}$$x - 2$$\textcolor{w h i t e}{a a a a a a}$$-$$\textcolor{w h i t e}{a a a a a a}$$+$

$\textcolor{w h i t e}{a a a a a}$$f \left(x\right)$$\textcolor{w h i t e}{a a a a a a a}$$-$$\textcolor{w h i t e}{a a a a a a}$$+$

Therefore,

$f \left(x\right) < 0$ when x in ] 2,+oo [