Mathematics · Ring Theory
Let f(x) = x3 - nx + 1 be a polynomial over ℤ. Select the correct statement:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f(x) is irreducible over ℤ for all values of n.
- 2f(x) is reducible over ℤ for all values of n.
- 3f(x) is reducible over ℤ if n ∈ {0, 2}.✓
- 4f(x) is reducible over ℤ for infinitely many values of n.
Correct answer
f(x) is reducible over ℤ if n ∈ {0, 2}.
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