Question

Show that a polynomial of degree 2 is reducible if it has roots.

score 2k · Answer 1 · 2015-11-25 21:19:54

2k

Views

Show that a polynomial of degree 2 is reducible if it has roots.

Published on 25 Nov 2015 - 21:19

score 183 · Answer 2 · 2026-04-03 19:55:21

183

Views

Artin's Algebra exercise special case of some theorem/problem?

Published on 03 Apr 2026 - 19:55

score 108 · Answer 3 · 2026-03-27 01:00:40

108

Views

Where is this formula about cyclotomic polynomials proved?

Published on 27 Mar 2026 - 1:00

score 2.6k · Answer 4 · 2015-11-27 02:41:35

2.6k

Views

Determine all of the monic irreducible polynomials in $\mathbb Z_3 [x]$ of degree $4.$

Published on 27 Nov 2015 - 2:41

score 80 · Answer 5 · 2015-11-28 22:46:54

Let $f$ be a polynomial with $\deg f = 2n + 1$, and $a_1, .\dots, a_{2n+1}$ that $f(a_i) \in \{+1, -1\}$. Show $f$ is irreducible

score 275 · Answer 6 · 2015-11-29 14:44:36

275

Views

Irreducibility in a polynomial related to quadratic residues

Published on 29 Nov 2015 - 14:44

score 104 · Answer 7 · 2015-11-30 02:05:45

104

Views

One root of the polynomial $f(x) = 5x^5+x^4-5x^3-x^2-10x-2$ over $\mathbb C$ is $i$.

Published on 30 Nov 2015 - 2:05

score 37 · Answer 8 · 2015-12-02 11:03:56

37

Views

Irreducibility of a polynomial in $k(y)[x]$

Published on 02 Dec 2015 - 11:03

score 34 · Answer 9 · 2015-12-05 21:27:15

34

Views

What to do if your characteristic equation is not fully reducible over your field when solving a recurrence relation?

Published on 05 Dec 2015 - 21:27

score 661 · Answer 10 · 2015-12-06 04:52:17

661

Views

For which monic irreducible $f(x)\in \mathbb Z[x]$ , is $f(x^2)$ also irreducible in $\mathbb Z[x]$?

Published on 06 Dec 2015 - 4:52

score 170 · Answer 11 · 2026-03-29 12:43:12

170

Views

Conflict between Gauss' theorem and the example $\mathbb{Z}[\sqrt{-5}]$

Published on 29 Mar 2026 - 12:43

score 296 · Answer 12 · 2015-12-07 14:03:26

296

Views

How can I prove that this quintic is irreducible in $\mathbb{Q}$?

Published on 07 Dec 2015 - 14:03

score 67 · Answer 13 · 2015-12-07 14:11:57

67

Views

$f \in \mathbb Z[x]$ be irreducible and suppose $f(x)$ has two roots in $\mathbb C$ with product $1$ , then degree of $f$ is even ?

Published on 07 Dec 2015 - 14:11

score 35 · Answer 14 · 2015-12-07 15:33:00

35

Views

If a polynomial have $n$ factors in $\mathbb{Z_p}$, does it have $n$ factors in $\mathbb{Q}$ if it is reducible?

Published on 07 Dec 2015 - 15:33

score 144 · Answer 15 · 2015-12-10 06:09:48

144

Views

Solving For $X$ In A 4th Degree Polynomial

Published on 10 Dec 2015 - 6:09

List Question

Show that a polynomial of degree 2 is reducible if it has roots.

Artin's Algebra exercise special case of some theorem/problem?

Where is this formula about cyclotomic polynomials proved?

Determine all of the monic irreducible polynomials in $\mathbb Z_3 [x]$ of degree $4.$

Let $f$ be a polynomial with $\deg f = 2n + 1$, and $a_1, .\dots, a_{2n+1}$ that $f(a_i) \in \{+1, -1\}$. Show $f$ is irreducible

Irreducibility in a polynomial related to quadratic residues

One root of the polynomial $f(x) = 5x^5+x^4-5x^3-x^2-10x-2$ over $\mathbb C$ is $i$.

Irreducibility of a polynomial in $k(y)[x]$

What to do if your characteristic equation is not fully reducible over your field when solving a recurrence relation?

For which monic irreducible $f(x)\in \mathbb Z[x]$ , is $f(x^2)$ also irreducible in $\mathbb Z[x]$?

Conflict between Gauss' theorem and the example $\mathbb{Z}[\sqrt{-5}]$

How can I prove that this quintic is irreducible in $\mathbb{Q}$?

$f \in \mathbb Z[x]$ be irreducible and suppose $f(x)$ has two roots in $\mathbb C$ with product $1$ , then degree of $f$ is even ?

If a polynomial have $n$ factors in $\mathbb{Z_p}$, does it have $n$ factors in $\mathbb{Q}$ if it is reducible?

Solving For $X$ In A 4th Degree Polynomial

Trending Questions

Popular # Hahtags

Popular Questions