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

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Answer 1 · 2016-12-28T09:57:34

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

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 $x in ] 2,+oo [$

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