Question

Prove implications of irreducible polynomial

score 76 · Answer 1 · 2019-10-02 22:32:15

76

Views

Prove implications of irreducible polynomial

Published on 02 Oct 2019 - 22:32

score 129 · Answer 2 · 2019-10-03 15:14:26

129

Views

Integer roots of polynomial with irrational coefficients

Published on 03 Oct 2019 - 15:14

score 132 · Answer 3 · 2019-10-03 21:42:30

132

Views

Irreducibility over $\Bbb Q$

Published on 03 Oct 2019 - 21:42

score 145 · Answer 4 · 2026-03-25 18:48:39

145

Views

Show that $1-999x^{888}\in \mathbb{Q}[x]$ is irreducible

Published on 25 Mar 2026 - 18:48

score 93 · Answer 5 · 2019-10-07 13:10:59

93

Views

Find prime fields over which a polynomial has roots.

Published on 07 Oct 2019 - 13:10

score 159 · Answer 6 · 2019-10-08 03:43:45

159

Views

Showing $x^4+x^3+2x+15$ is irreducible in $\mathbb{Q}[x]$

Published on 08 Oct 2019 - 3:43

score 1.4k · Answer 7 · 2019-10-08 19:39:45

1.4k

Views

Prove that any polynomial $f(x)\in K[X]$, where $K$ is a field, can be uniquely factored into a product of irreducible polynomials times a constant.

Published on 08 Oct 2019 - 19:39

score 331 · Answer 8 · 2019-10-09 05:05:29

331

Views

$x^5-2x^3+2x-2$ irreducible over $\mathbb{Q}(\sqrt[3]{2})$

Published on 09 Oct 2019 - 5:05

score 57 · Answer 9 · 2019-10-10 13:33:31

57

Views

$K/k$ field extension, $[K:k]=n,f(x)\in k[x]$ irreducible over $k$ with degree $m$, and $f$ has a root in $K\implies m$ divides $n$

Published on 10 Oct 2019 - 13:33

score 44 · Answer 10 · 2019-10-11 02:31:08

44

Views

Finding the degree $[\mathbb{Q}(\sqrt[4]{3},\sqrt[5]{3}):\mathbb{Q}]$

Published on 11 Oct 2019 - 2:31

score 59 · Answer 11 · 2019-10-11 06:30:14

59

Views

Specific elements of a ring

Published on 11 Oct 2019 - 6:30

score 178 · Answer 12 · 2019-10-12 15:36:14

178

Views

Reducible polynomials similar to Sophie Germain's identity

Published on 12 Oct 2019 - 15:36

score 665 · Answer 13 · 2019-10-12 23:46:05

665

Views

With the goal of having a function defined for all values of x, why can you only sometimes simplify a fraction, making divisor not equal zero?

Published on 12 Oct 2019 - 23:46

score 40 · Answer 14 · 2019-10-13 03:22:18

40

Views

Proving that there are infinitely many primes $p$ that $x^2-2$ is irreducible over $\mathbb{Z}_p[x]$ .

Published on 13 Oct 2019 - 3:22

score 429 · Answer 15 · 2019-10-13 11:20:24

429

Views

Prove, that $p\in\mathbb{R}[x]$ with $p=x^2+ax+b$ is irreducible if and only if $a^2<4b$.

Published on 13 Oct 2019 - 11:20

List Question

Prove implications of irreducible polynomial

Integer roots of polynomial with irrational coefficients

Irreducibility over $\Bbb Q$

Show that $1-999x^{888}\in \mathbb{Q}[x]$ is irreducible

Find prime fields over which a polynomial has roots.

Showing $x^4+x^3+2x+15$ is irreducible in $\mathbb{Q}[x]$

Prove that any polynomial $f(x)\in K[X]$, where $K$ is a field, can be uniquely factored into a product of irreducible polynomials times a constant.

$x^5-2x^3+2x-2$ irreducible over $\mathbb{Q}(\sqrt[3]{2})$

$K/k$ field extension, $[K:k]=n,f(x)\in k[x]$ irreducible over $k$ with degree $m$, and $f$ has a root in $K\implies m$ divides $n$

Finding the degree $[\mathbb{Q}(\sqrt[4]{3},\sqrt[5]{3}):\mathbb{Q}]$

Specific elements of a ring

Reducible polynomials similar to Sophie Germain's identity

With the goal of having a function defined for all values of x, why can you only sometimes simplify a fraction, making divisor not equal zero?

Proving that there are infinitely many primes $p$ that $x^2-2$ is irreducible over $\mathbb{Z}_p[x]$ .

Prove, that $p\in\mathbb{R}[x]$ with $p=x^2+ax+b$ is irreducible if and only if $a^2<4b$.

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