Showing that every polynomial over the Algebraic Numbers has a $0$ in the Algebraic Numbers.
31831
Why every polynomial over the algebraic numbers $F$ splits over $F$?
13981
Proof that every polynomial of odd degree has one real root
109102
Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
10514
Proof that no polynomial with integer coefficients can only produce primes
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
89553
proof that every finite matrix has an annihilating polynomial
152347
Proof that a certain entire function is a polynomial
81682
Proving the algebraic set corresponding to a polynomial is infinite.
33696
A polynomial is zero if it zero on infinite subsets
100862
Polynomials with rational zeros
55119
Proof that the coefficients of a polynomial are real
12402
Showing a function on $[0,1]$ is the zero function
47266
Every affine variety in $\mathbb A^n$ consisting of finitely many points can be written as the zero locus of $n$ polynomials
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
134342
Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.