Prove that the polynomial is irreducible over Hence construct

a field F with 25 elements which extends . Does the polynomial have

a zero in F? In other words, you need to find all the solutions (if any) to the equation

in F.

My attempt.

has no zero thus irreducible over (treid x=0,1,2,3,4)How do i construct field with 25 elements?

has no zero in F because this polynomial is also Irreducible over How do i find solution to

in F?

Thank you in advance.