Proving a cubic polynomial has no rational roots
30511
Monic $f(x)\in\Bbb Z[x]$ has no rational root if $f(0)\ \&\ f(1)$ odd [Parity Root Test, Modular Root Test]
139288
Formal proof that $e^x$ is not algebraic
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
40994
How to check that a cubic polynomial is irreducible?
53139
How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
147158
Galois group of a non-separable polynomial
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
54875
How to prove polynomials with degree $n$ does not form a vector space?
121373
Elementary Symmetric Polynomials, Roots of cubic polynomials
2408
Show that a polynomial has at least one positive solution/root.
152347
Proof that a certain entire function is a polynomial
11329
Proving a graph has no Hamiltonian cycle
130823
cubic equations which have exactly one real root
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
88466
Show that polynomial $X^{n+1}-aX^n+aX-1$ has only roots of module $1$