[Start of training sample]
The following are multiple choice examples (questions with answers) about  abstract algebra.

Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
A. 0
B. 1
C. 2
D. 3
Answer: B

Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: B

Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: C

Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: A

Find the characteristic of the ring 2Z.
A. 0
B. 3
C. 12
D. 30
Answer: A

[End of training sample]

Only output the answer to the following question:
Find the product of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].
A. 2x^2 + 5
B. 6x^2 + 4x + 6
C. 0
D. x^2 + 1
Answer: Provide exactly two different responses that are separated with 6 asterisk symbols: ******.
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