Irreducibility criteria (Eisenstein)
General · Mathematics
Study notes
Q: Prove x³-2 is irreducible over ℚ using Eisenstein. p = 2: 2 | 0 (x², x coeffs) ✓, 2 ∤ 1 (leading) ✓, 2² = 4 ∤ -2 ✓. Eisenstein: IRREDUCIBLE over ℚ! (∛2: irrational - degree 3!) Contrast: x²-4 = (x-2)(x+2): reducible!