Show that there is a unique polynomial of degree at most $2k+1$ such that $p^{[j]}(x_1)=a_j \text{ and } p^{[j]}(x_2)=b_j \text{ for } j=0,\dots, k.$
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
89473
Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
102432
Irreducible polynomial of degree $8$
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
70537
Irreducible polynomials have distinct roots?
157487
Showing a polynomial having at least one integer root under certain conditions has precisely one integer root
54212
Another polynomial equation
84697
Show that if $|f(z)| \leq M |z|^n$ then $f$ is a polynomial max degree n
35959
irreducibility of a polynomial over $\mathbb{F}_2$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
103552
The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
146312
Is the set of roots with respect to their values and multiplicies unique for each $g(x)$ in $a_n x^n + g(x)$?
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension