Show that the minimal polynomial $f(x) $ has $\deg f(x)=5$
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
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 $k=0, \dots, n$.
103340
Show that this entire function is polynomial.
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
48873
Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$.
55232
Show that $g\circ f\equiv 0$ implies $\det Df\equiv 0$, where $g(x_1,...,x_n)=x_1^5+...+x_n^5$
145191
Content of a polynomial
126197
Prove that $T$ has a cyclic vector iff its minimal and characteristic polynomials are the same
109721
The number of zeros in a polynomial
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
109952
Find the minimal polynomial of $\sqrt2 + \sqrt3 $ over $\mathbb Q$
26999
How is the degree of the minimal polynomial related to the degree of a field extension?
14111
Determining possible minimal polynomials for a rank one linear operator
82295
Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem
6722
to show $f$ is a polynomial in $z$