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Irreducible-polynomials
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How to check that a cubic polynomial is irreducible?
August 1st, 2022
irreducible-polynomials
finite-fields
polynomials
abstract-algebra
Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible.
August 1st, 2022
polynomials
abstract-algebra
irreducible-polynomials
Does the Rational Root Theorem ever guarantee that a polynomial is irreducible?
August 1st, 2022
roots
irreducible-polynomials
abstract-algebra
polynomials
Decomposition of polynomial into irreducible polynomials
August 1st, 2022
abstract-algebra
polynomials
irreducible-polynomials
Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
August 1st, 2022
number-theory
irreducible-polynomials
$X^4-4X^2-1$ irreducible over $\mathbb{Q}[X]$
April 14th, 2022
abstract-algebra
polynomials
field-theory
irreducible-polynomials
How to find all irreducible polynomials in Z2 with degree 5?
August 1st, 2022
irreducible-polynomials
abstract-algebra
finite-fields
Show that $\mathbb{Q}(\sqrt{5}+\sqrt[3]{2})=\mathbb{Q}(\sqrt{5},\sqrt[3]{2})$.
August 1st, 2022
irreducible-polynomials
extension-field
polynomials
field-theory
abstract-algebra
Quotient $K[x,y]/(f)$, $f$ irreducible, which is not UFD
January 9th, 2020
unique-factorization-domains
irreducible-polynomials
abstract-algebra
Showing that $x^4 -2x^2 +8 x+1$ is irreducible over $\Bbb Q$
August 1st, 2022
irreducible-polynomials
polynomials
factoring
Galois group of irreducible cubic equation
August 1st, 2022
abstract-algebra
galois-theory
irreducible-polynomials
splitting-field
Irreducible $f(x) \in F[x]$ of prime degree, $E/F$ finite extension, $p \mid [E:F]$.
August 1st, 2022
abstract-algebra
irreducible-polynomials
extension-field
field-theory
Determine splitting field $K$ over $\mathbb{Q}$ of the polynomial $x^3 - 2$
August 1st, 2022
roots-of-unity
splitting-field
irreducible-polynomials
field-theory
Homogeneous polynomial in $k[X,Y,Z]$ can factor into linear polynomials?
August 1st, 2022
commutative-algebra
polynomials
algebraic-geometry
irreducible-polynomials
abstract-algebra
Why is it that $x^4+2x^2+1$ is reducible in $\mathbb{Z}[x]$ but has no roots in $\mathbb{Q}$?
March 9th, 2020
roots
abstract-algebra
ring-theory
irreducible-polynomials
$R = \mathbb{Z}[\sqrt{-41}]$, show that 3 is irreducible but not prime in $R$
August 1st, 2022
prime-numbers
irreducible-polynomials
unique-factorization-domains
Nature of roots of a biquadratic equation
August 1st, 2022
polynomials
graphing-functions
irreducible-polynomials
algebra-precalculus
roots
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