Ok, so all the algebra work has been done
I would look at the graph of
y = x^3-5x^2+2x+8
I know that this is standard cubic function opening up in quadrant I and having x-intercepts of -1, 2, and 4
So a very rough sketch shows me that this curve is below the x-axis ( < 0 ) for x < - 1 or 2 < x < 4
looking at all cases , the critical values of -2,2, and 4 split the line into 4 parts :
if x < -1, try some value, e.g. x = -5
(-)(-)(+) < 0 , so yes
x < -1
if x is between -2 and 2 , e.g. x = 0
(+)(-)(-2) > 0 , so NO
if x is between 2 and 4 , e.g. x = 3
(+)(-)(+) < 0 , so YES
x is between 2 and 4
if x > 4 , e.g. x = 5
(+)(+)(+) > 0 , NO
then x < -2 OR 2 < x < 4
Reiny help me with using intervals. u forgot to help me with that. its urgent please
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