Simplifying
4p4 + -5p2 + 1

Reorder the terms:
1 + -5p2 + 4p4

Factor a trinomial.
(1 + -4p2)(1 + -1p2)

Factor a difference between two squares.
((1 + 2p)(1 + -2p))(1 + -1p2)

Factor a difference between two squares.
((1 + p)(1 + -1p))(1 + 2p)(1 + -2p)

Final result:
(1 + 2p)(1 + -2p)(1 + p)(1 + -1p)