Is $x^4 +15x +25$ irreducible over $\mathbb{Q}[x]$?
The Eisenstein criterion does not help because $5^2 \mid 25$. Which criterion can I use?
2026-04-07 22:58:01.1775602681
Is $x^4 +15x +25$ irreducible in $\mathbb{Q}[x]$?
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The polynomial $x^4 + 15x + 25$ is strictly positive and thus has no roots in $\mathbb{R}$. So if it is reducible we can write $x^4 + 15x + 25 = (x^2 + ax + b)(x^2 + cx + d)$. Try to derive a contradiction from this.