List questions from polynomials

Published on 25 Mar 2026 - 7:40

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How does one prove that $(x^4 - 5)$ and $(x^4 + 5)$ are irreducible over $\mathbb{Q}$?

Published on 25 Mar 2026 - 5:03

499

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Galois group as permutations of roots

Published on 27 Mar 2026 - 14:31

78

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Finding square root of given expression

Published on 08 Apr 2018 - 11:19

281

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Is this rule for the bracket polynomial redundant?

Published on 26 Mar 2026 - 3:47

1.1k

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Let $F$ be a field. Show that if $p(x)$ is divided by $x-a$, the remainder is $p(a)$.

Published on 27 Mar 2026 - 20:21

2.6k

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If $F$ is a field, show that $F[x]$ is never a field.

Published on 27 Mar 2026 - 20:21

44

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Fidning roots of an arbitrary polynomial with a specific pattern

Published on 25 Mar 2026 - 6:01

41

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sum (difference) of polynomials to the power n

Published on 08 Apr 2018 - 21:10

275

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Show that the ring isomorphism $\phi :R[x]\to S[x]$ is well-defined.

Published on 25 Mar 2026 - 23:40

115

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If one root of $ax^2 + bx + c$ is double the other, then we must have $ 2b^2 = 9 ac $.

Published on 09 Apr 2018 - 2:41

68

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"A Cubic Function From the Reals to the Reals is Always Injective": False?

Published on 24 Mar 2026 - 22:01

1.2k

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Writing a polynomial as a product of two other polynomials?

Published on 09 Apr 2018 - 17:20

74

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Dividing polynomials in $\mathbb{F}_7[x]$

Published on 27 Mar 2026 - 20:12

115

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How I show this :$\sum_{k,j=0}^{n}\frac{a_k a_j}{k+j+1} \leq \pi \sum_{k=0}^{n}a_k^2$?

Published on 09 Apr 2018 - 23:09

List Question

Factoring polynomials given one obvious factor

How does one prove that $(x^4 - 5)$ and $(x^4 + 5)$ are irreducible over $\mathbb{Q}$?

Galois group as permutations of roots

Finding square root of given expression

Is this rule for the bracket polynomial redundant?

Let $F$ be a field. Show that if $p(x)$ is divided by $x-a$, the remainder is $p(a)$.

If $F$ is a field, show that $F[x]$ is never a field.

Fidning roots of an arbitrary polynomial with a specific pattern

sum (difference) of polynomials to the power n

Show that the ring isomorphism $\phi :R[x]\to S[x]$ is well-defined.

If one root of $ax^2 + bx + c$ is double the other, then we must have $ 2b^2 = 9 ac $.

"A Cubic Function From the Reals to the Reals is Always Injective": False?

Writing a polynomial as a product of two other polynomials?

Dividing polynomials in $\mathbb{F}_7[x]$

How I show this :$\sum_{k,j=0}^{n}\frac{a_k a_j}{k+j+1} \leq \pi \sum_{k=0}^{n}a_k^2$?

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