Newbetuts

Showing that minimal polynomial has the same irreducible factors as characteristic polynomial [duplicate]

How do you show that the degree of an irreducible polynomial over the reals is either one or two?

An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension

Are derivatives of geometric progressions all irreducible?

How can I prove irreducibility of polynomial over a finite field?

Quotient ring $\frac{\mathbb{Z}_n[x]}{⟨f(x)^2⟩}$

$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$

Prove that the polynomial $x^nf(1/x)$ with reverted coefficients is also irreducible polynomial over $\mathbb{Q}$

How to prove that $f(x)=(x-1)^2(x-2)^2(x-3)^2\cdots(x-2013)^2+2014$ is reducible?

Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$

Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible

How many irreducible factors does $x^n-1$ have over finite field?

Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.

Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$

New posts in irreducible-polynomials

Irreducible polynomial means no roots?

Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$

Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?

Maximum possible number of extrema of the function?

Galois groups of $x^3-3x+1$ and $(x^3-2)(x^2+3)$ over $\mathbb{Q}$

Proving/disproving $\{a^{k_1}\}=\{a^{k_2}\}=\{a^{k_3}\}$

Showing that minimal polynomial has the same irreducible factors as characteristic polynomial [duplicate]

How do you show that the degree of an irreducible polynomial over the reals is either one or two?

An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension

Are derivatives of geometric progressions all irreducible?

How can I prove irreducibility of polynomial over a finite field?

Quotient ring $\frac{\mathbb{Z}_n[x]}{⟨f(x)^2⟩}$

$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$

Prove that the polynomial $x^nf(1/x)$ with reverted coefficients is also irreducible polynomial over $\mathbb{Q}$

How to prove that $f(x)=(x-1)^2(x-2)^2(x-3)^2\cdots(x-2013)^2+2014$ is reducible?

Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$

Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible

How many irreducible factors does $x^n-1$ have over finite field?

Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.

Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$