1. All three numbers are negative. The easiest way to make all three numbers negative is to make the largest number negative. (Think about a number line. Larger numbers are to the right and smaller numbers are to the left. If (p+4) is negative (left of 0) and if p and (p-4) are to the left of (p+4), won't p and (p-4) also be the the left of 0 (negative)?) So:
will make all three numbers negative. Subtracting 4 from both sides we get
This is part 1 of our solution.
2. Two numbers are positive and one is number is negative. This can only happen if the smallest number is negative and the other two are positive. (Think about it.) Using logic like the earlier solution we can make the two larger numbers positive by making the "in between" number positive. So to get one negative factor and two positive factors if both of the following are true:
Adding 4 to both sides of the first inequality we get
This is the second part of the solution.
The complete solution is:
[[[p < -4 or (p <= 4 and p >= 0)}}}
In words, "p" must be a number less than -4 OR "p" must be a number between 0 and 4 (inclusive).