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 [ #