Question

I need help finding the solution set for this problem.

(x+16)(x-18)(x+5)>0
The Solution set is {x|___}

Answer 1

first what are the zeros of
\[f(x)=(x+16)(x-18)(x+5)\]

Answer 2

I will give you a hint there are 3 zeros

Answer 3

totally lost

Answer 4

what x makes f=0
what about x=-16?
when you plug that in, isn't the first factor then equal to zero?

Answer 5

so that is one zero
can you see the other two now?

Answer 6

I see, so how do I plug the answer {x| ____} in here?

Answer 7

we haven't got there

Answer 8

so what are the other two zeros?

Answer 9

18, -5

Answer 10

good!

Answer 11

-----|-----|-----|-----
-16 -5 18

so we need to test these intervals to see if we have f>0 or if f<0

Answer 12

ok

Answer 13

so try pluggin and -18 into f
and plug in -10 into f
and plug in 0 into f
and plug in 20 into f

just choose a number in each interval

Answer 14

honestly I don't know

Answer 15

we need to test (-inf,-16) choose a number in this interval and plug into f
we need to test (-16,-5) choose a number in this interval and plug into f
we need to test (-5,18) choose a number in this interval and plug into f
we need to test (18,inf) choose a number in this interval and plug into f

Answer 16

for example in that first interval I mention a number in that interval is -18
so I will plug -18 into f
recall
\[f(x)=(x+16)(x-18)(x+5) \]
\[f(-18)=(-18+16)(-18-18)(-18+5)=(-)(-)(-)=(-) <0\]

Answer 17

you want to try the next interval

Answer 18

WOW this is so complicated for me at this time at night. LOL

Answer 19

i just replaced the x's with -18
i didn't really care about getting the actually number that that mess equaled
i was trying to decide if f(-18) was going to be positive or negative

Answer 20

-18+16= negative
-18-18=negative
-18+5=negative
the product of these outcomes is negative right
negative numbers are less than 0
so thats why you see <0

Answer 21

Thank you! I will try tomorrow I honestly can think right now.

Answer 22

Ok goodnight!