Irreducible polynomial proof
106374
Show that $2x^6+12x^5+30x^4+60x^3+80x^2+30x+45=0$ has no real roots
141792
Slick proof the determinant is an irreducible polynomial
63605
Irreducible polynomials and affine variety
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
112371
Computing irreducible components of algebraic set
10885
Existence of irreducible polynomials over finite field
52528
Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
55119
Proof that the coefficients of a polynomial are real
12166
How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
120673
Irreducible fibers of a closed subset implies irreducibility
140808
Problem on Galois theory and irreducible polynomial