Exercise
The product of X2 + 1 + (X3) and X2 + (X3) in Q[X]/(X3) is
0 + (X3)
X2 + (X3)
X4 + (X3)
No, for (X2 + 1)X2 is not
divisible by X3.
Yes, (X2 + 1)X2 is congruent
to X2 modulo X3.
No, (X2 + 1)X2 is not congruent
to X4 modulo X3.