# How do you solve x^2-4x-32>0 using a sign chart?

Nov 12, 2016

The answer is x in] -oo,-4 [ uu ] 8, oo[

#### Explanation:

Let's factorise the expression $f \left(x\right) = {x}^{2} - 4 x - 32 = \left(x - 8\right) \left(x + 4\right)$

let's do the sign chart

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a}$$- 4$$\textcolor{w h i t e}{a a a a}$$8$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x + 4$$\textcolor{w h i t e}{a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$x - 8$$\textcolor{w h i t e}{a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

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

Therefore, $f \left(x\right) > 0$ when  x in] -oo,-4 [ uu ] 8, oo[

graph{x^2-4x-32 [-74, 74.05, -37, 37.14]}