Can someone help me factor this problem?

Question

Generally I wouldn't have a problem doing it, but today we're supposed to factor problems without knowing what exactly to do, (Trinomial squares, difference of squares, magic diamond, etc), and it's really stumping me.
For exampled I'm stuck on this one,
p^5 + 3p^3 + p^2 + 3

Answer 1

p^5 + p^2 + 3 (p^3+1)

p^2 (p^3+1) + 3(p^3+1)

(p^2+3)(p^3+1)