Part CCSIR NET December 2025eisenstein-only-blesses-the-cubic-the-other-two-quadratics-factor-by-inspection

Eisenstein only blesses the cubic the other two quadratics factor by inspection

Which of the following statements are true?

A. $x^{2} +$ xy $^{2} - x - y + 1$ is irreducible in $\mathbb{Q}[x,y]$ .✓
B. $x^{3} + 100x^{2} + 25x + 10$ is irreducible in $\mathbb{Z}[x]$ .✓
C. $2x^{2} + 3$ xy $+ y^{2} + 3x + 2y + 1$ is irreducible in $\mathbb{Q}[x,y]$ .
D. $x^{4} + 4x^{2} + 3$ is irreducible in $\mathbb{Z}[x]$ .

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

50 are analysed free — try those first.

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