query: $f=X^p-a\in F[X]$ is irreducible iff $f$ has no root in $F$
positive_passages.docid: 18336
positive_passages.text: $x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
negative_passages.docid: 28658
negative_passages.text: $R$ with an upper bound for degrees of irreducibles in $R[x]$
negative_passages.docid: 24626
negative_passages.text: Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
negative_passages.docid: 93196
negative_passages.text: $x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$
negative_passages.docid: 151961
negative_passages.text: Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
negative_passages.docid: 26069
negative_passages.text: Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
negative_passages.docid: 102422
negative_passages.text: Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
negative_passages.docid: 115299
negative_passages.text: Elements of $\mathbb{F}_p$ having cube roots in $\mathbb{F}_p$
negative_passages.docid: 70249
negative_passages.text: Irreducibility of Polynomials in $k[x,y]$
negative_passages.docid: 44502
negative_passages.text: An irreducible polynomial cannot share a root with a polynomial without dividing it
negative_passages.docid: 41693
negative_passages.text: Use irreducible fibers to show $X$ is irreducible
negative_passages.docid: 112427
negative_passages.text: Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
negative_passages.docid: 132572
negative_passages.text: Why this polynomial is irreducible?
negative_passages.docid: 74224
negative_passages.text: On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
negative_passages.docid: 53012
negative_passages.text: Irreducibility of a polynomial if it has no root (Capelli)
negative_passages.docid: 16035
negative_passages.text: Irreducibility of $X^{p-1} + \cdots + X+1$
negative_passages.docid: 134701
negative_passages.text: Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$