List questions from polynomials

Published on 01 Jul 2018 - 12:08

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Let $p(x) \in \mathbb{Z}[x], p(2) = p(-2) = 2, p(100) < 0$. Prove that $p(100) < -1000$

Published on 01 Jul 2018 - 13:47

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Is there a converse of Abhyankar-Moh-Suzuki theorem?

Published on 30 Mar 2026 - 9:52

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Determining the roots of polynomial $R(x)$

Published on 02 Jul 2018 - 8:05

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Show that a map $f\in C^1(\mathbb{C})$ is a polynomial of a degree less or equal to $n$.

Published on 02 Jul 2018 - 11:29

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Solution of polynomial

Published on 02 Jul 2018 - 13:40

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Yun's algorithm and integers

Published on 25 Mar 2026 - 17:17

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Show that $f=\sum_{j=0}^{n}f_jx^j$ for $f\in R[x]$ and $f_i=0$ for all $i>n$.

Published on 30 Mar 2026 - 12:43

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obtain polynomials $P(y)$ for specific data

Published on 02 Jul 2018 - 18:46

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Find all polynomials $P(x)$ with the property that $P(x)$ is a multiple of $P''(x).$

Published on 02 Jul 2018 - 23:07

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Is there a name for "almost-subspaces" $U$ that do not satisfy $cu \in U, \forall u \in U$? If so do they have any properties?

Published on 24 Mar 2026 - 22:14

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Is there a real number exceeds cube by $1$

Published on 03 Jul 2018 - 3:14

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How to derive this factorization $ax^2 + bx + c = a(x − x_1)(x − x_2) $?

Published on 25 Mar 2026 - 18:51

50

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Confusion about roots

Published on 30 Mar 2026 - 17:07

453

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Scalar extension in polynomial ring

Published on 28 Mar 2026 - 6:14

List Question

Inequality in $n$-variables

Let $p(x) \in \mathbb{Z}[x], p(2) = p(-2) = 2, p(100) < 0$. Prove that $p(100) < -1000$

Is there a converse of Abhyankar-Moh-Suzuki theorem?

Determining the roots of polynomial $R(x)$

Show that a map $f\in C^1(\mathbb{C})$ is a polynomial of a degree less or equal to $n$.

Solution of polynomial

Yun's algorithm and integers

Show that $f=\sum_{j=0}^{n}f_jx^j$ for $f\in R[x]$ and $f_i=0$ for all $i>n$.

obtain polynomials $P(y)$ for specific data

Find all polynomials $P(x)$ with the property that $P(x)$ is a multiple of $P''(x).$

Is there a name for "almost-subspaces" $U$ that do not satisfy $cu \in U, \forall u \in U$? If so do they have any properties?

Is there a real number exceeds cube by $1$

How to derive this factorization $ax^2 + bx + c = a(x − x_1)(x − x_2) $?

Confusion about roots

Scalar extension in polynomial ring

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