Given a polynomial $$x^3-120x+p$$, where $p$ is a prime number, how do you find all $p$ values that make the polynomial reducible in the rational numbers?
2026-03-25 15:52:36.1774453956
Given $x^3-120x+p$, find all $p$ that make the polynomial reducible
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$p=x(120-x^2)$ for an integer $x$, which gives $x\in\{1,-1\}$ or $120-x^2\in\{1,-1\},$
which gives $x=-11$ and $p=11$.