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Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.

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Irreducibility of the polynomial $x^n+5x+3$ over $\mathbb{Q}$

Note: I used Matlab to calculate the circumstance $1<n\le 100$, the result says all of these polynomials are irreducible. …