How do you solve #(a-2)(a+4)>0#?

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Answer 1 · 2016-12-05T16:15:12

The answer is #x in ] -oo,-4 [ uu ] 2,+oo [#

Let #f(a)=(a-2)(a+4)#

Then we do a sign chart

#color(white)(aaaa)##a##color(white)(aaaa)##-oo##color(white)(aaaa)##-4##color(white)(aaaa)##2##color(white)(aaaa)##+oo#

#color(white)(aaaa)##a+4##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##a-2##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##f(a)##color(white)(aaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#

For #f(a)>0#, #x in ] -oo,-4 [ uu ] 2,+oo [#