Question 150646
{{{p^4 -1}}} is a difference of two squares.
{{{(p^2 -1)(p^2+1)}}} 

Now note that {{{p^2-1}}} is also a difference of two squares. So you can factor that the same way
{{{(p^2 -1)(p^2+1)}}} 
{{{(p-1)(p+1)(p^2+1)}}}

It is possible to factor {{{p^2+1}}} using the quadratic equation. The resulting factors contain complex roots. Unless you are at the point where you know imaginary numbers, you don't need to factor {{{p^2+1}}} past where it is now.