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.