SOLUTION: List all the polynomials of degree exactly two in Z3[t]. Which of these are reducible, which are irreducible note: Z stands for Integers

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Question 31161: List all the polynomials of degree exactly two in Z3[t]. Which of these are reducible, which are irreducible
note: Z stands for Integers
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
2) list all the polynomials of degree exactly two in Z3[t]. Which of these
> are reducible, which are irreducible?
AT^2+BT+C FOR VARIOUS VALUES OF A,B,C ARE POLYNOMIALS OF DEGREE 2 IN VARIANT T.
WE CAN EASILY SEE THAT FOR A=1,B=1,C=-1
F(T)=T^2+T-1 IS NOT REDUCIBLE IN Z3,SINCE
F(0),F(1),F(-1),F(2),F(-2) ARE ALL NOT EQUAL TO
ZERO(MOD3)