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Start with the given inequality
Factor the left side
Set the left side equal to zero
Set each individual factor equal to zero:
or
Solve for p in each case:
or
So our critical values are
and
Now set up a number line and plot the critical values on the number line
So let's pick some test points that are near the critical values and evaluate them.
Let's pick a test value that is less than
(notice how it's to the left of the leftmost endpoint):
So let's pick
Start with the given inequality
Plug in
Evaluate and simplify the left side
Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.
So part our solution in interval notation is
(
)
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Let's pick a test value that is in between
and
:
So let's pick
Start with the given inequality
Plug in
Evaluate and simplify the left side
Since the inequality is false, this means that the interval does
not work. So this interval is
not in our solution set and we can ignore it.
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Let's pick a test value that is greater than
(notice how it's to the right of the rightmost endpoint):
So let's pick
Start with the given inequality
Plug in
Evaluate and simplify the left side
Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.
So part our solution in interval notation is
(
)
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Summary:
So the solution in interval notation is:
() 
()
(