Question

Show that $x-1$ is a factor of $P(x)$ where $P(x^5)+xQ(x^5)+x^2R(x^5)=\big(x^4+x^3+x^2+x+1\big)S(x)$

score 168 · Answer 1 · 2026-03-27 05:41:48

168

Views

Show that $x-1$ is a factor of $P(x)$ where $P(x^5)+xQ(x^5)+x^2R(x^5)=\big(x^4+x^3+x^2+x+1\big)S(x)$

Published on 27 Mar 2026 - 5:41

score 2.9k · Answer 2 · 2026-03-25 16:13:44

2.9k

Views

Prove that the polynomial $x^5+2x+1$ is irreducible over $\mathbb{Z}$.

Published on 25 Mar 2026 - 16:13

score 69 · Answer 3 · 2026-03-30 02:11:34

69

Views

What is the meaning of $p(\cdot)$?

Published on 30 Mar 2026 - 2:11

score 161 · Answer 4 · 2026-03-25 04:44:20

161

Views

How to minimize the following polynomial over a four-dimensional sphere: $(c_0x_0^2+c_1x_1^2+c_2x_2^2+c_3x_3^2)^2+\sum_{nm}c_{nm} x_nx_m $

Published on 25 Mar 2026 - 4:44

score 105 · Answer 5 · 2018-08-05 06:54:21

105

Views

Increasing and decreasing intervals

Published on 05 Aug 2018 - 6:54

score 133 · Answer 6 · 2026-03-25 06:21:04

133

Views

Can we solve $A+D\sin^{2}x=B\sin x+C\cos x$ without having to solve a quartic polynomial?

Published on 25 Mar 2026 - 6:21

score 332 · Answer 7 · 2026-03-25 06:20:59

332

Views

Let $P(x)=x^2+bx+c$, where $b$ and $c$ are integers.

Published on 25 Mar 2026 - 6:20

score 505 · Answer 8 · 2026-03-25 14:22:37

505

Views

symmetric polynomial recursion to solve the system, $x^5+y^5=33$, $x+y=3$

Published on 25 Mar 2026 - 14:22

score 763 · Answer 9 · 2026-03-25 17:51:57

763

Views

Minimal polynomials of elements in $\mathbb F_{16}$

Published on 25 Mar 2026 - 17:51

score 1.1k · Answer 10 · 2026-03-29 08:56:12

1.1k

Views

Differential Polynomials(?)

Published on 29 Mar 2026 - 8:56

score 103 · Answer 11 · 2026-03-30 20:40:32

103

Views

Computing the kernel of a morphism whose domain and codomain are polynomial algebras

Published on 30 Mar 2026 - 20:40

score 373 · Answer 12 · 2026-03-31 16:26:54

373

Views

If the roots of the equation $x^2 + 3x -1 = 0$ also satisfy the equation $x^4 + ax^2 + bx + c = 0$ find the value of $a + b + 4c + 100$

Published on 31 Mar 2026 - 16:26

score 71 · Answer 13 · 2026-03-31 17:54:21

71

Views

Let $l$ be the minimum value of $2(y-2)^2 +4(x -7)^2 +(y+4)^2$. Find $[2018/l]$ where $[\cdot]$ is the greatest integer function.

Published on 31 Mar 2026 - 17:54

score 492 · Answer 14 · 2018-08-06 16:47:18

492

Views

Determine whether S is a subspace of $P_n$, the vectorspace of all real polynomial

Published on 06 Aug 2018 - 16:47

score 2.4k · Answer 15 · 2026-03-25 16:13:45

2.4k

Views

$x^4+x^3+x^2+x+1$ irreducible over $\mathbb F_7$

Published on 25 Mar 2026 - 16:13

List Question

Show that $x-1$ is a factor of $P(x)$ where $P(x^5)+xQ(x^5)+x^2R(x^5)=\big(x^4+x^3+x^2+x+1\big)S(x)$

Prove that the polynomial $x^5+2x+1$ is irreducible over $\mathbb{Z}$.

What is the meaning of $p(\cdot)$?

How to minimize the following polynomial over a four-dimensional sphere: $(c_0x_0^2+c_1x_1^2+c_2x_2^2+c_3x_3^2)^2+\sum_{nm}c_{nm} x_nx_m $

Increasing and decreasing intervals

Can we solve $A+D\sin^{2}x=B\sin x+C\cos x$ without having to solve a quartic polynomial?

Let $P(x)=x^2+bx+c$, where $b$ and $c$ are integers.

symmetric polynomial recursion to solve the system, $x^5+y^5=33$, $x+y=3$

Minimal polynomials of elements in $\mathbb F_{16}$

Differential Polynomials(?)

Computing the kernel of a morphism whose domain and codomain are polynomial algebras

If the roots of the equation $x^2 + 3x -1 = 0$ also satisfy the equation $x^4 + ax^2 + bx + c = 0$ find the value of $a + b + 4c + 100$

Let $l$ be the minimum value of $2(y-2)^2 +4(x -7)^2 +(y+4)^2$. Find $[2018/l]$ where $[\cdot]$ is the greatest integer function.

Determine whether S is a subspace of $P_n$, the vectorspace of all real polynomial

$x^4+x^3+x^2+x+1$ irreducible over $\mathbb F_7$

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