``Conway polynomials'' are irreducible polynomials over Zp that Sage (and other software) uses to build maximal ideals in polynomial rings, and thus quotient rings that are fields. Roughly speaking, they are ``canonical'' choices for each degree and each prime. The command conway\_polynomial(p, n) will return a database entry that is an irreducible polynomial of degree n over Zp.
Execute the command conway\_polynomial(5, 4) to obtain an allegedly irreducible polynomial of degree 4 over Z5: p=x4+4x2+4x+2. Construct the right polynomial ring (i.e., in the indeterminate x) and verify that p is really an element of your polynomial ring.
First determine that p has no linear factors. The only possibility left is that p factors as two quadratic polynomials over Z5. Use a list comprehension with three for statements to create every possible quadratic polynomial over Z5. Now use this list to create every possible product of two quadratic polynomials and check to see if p is in this list.