The fastest way to solve this problem is to plot a graph. I would love to help but I lack right now the resources to post a picture.
I believe that Bunuel will soon show up and help us.
I will try to explain anyway:
(1) Consider three parallel number lines
(p) , one for \(p^3\), one for \(1-p^2\) and a third one to represent the product of the these two functions. The "+" and "-" represents the sign
(Y) of the functions.
A: \(p^3\):-------(-1)---0+++(+1)++++
B: \(1-p^2\):----(-1)+++0+++(+1)-----
A*B:++++++++(-1)---0+++(+1)----- -->
So p can be either positive or negative = Insuff.(2) \(p^2 - 1\) ++++(-1)---(0)---(+1)++++++
Same as in (1), p can be either positive or negative = Insuff.(1) and (2) together shows a clear intersection when p < 0, so Suff.