Question

if in the expansion of $(1+x)^m (1-x)^n$, the coefficients of $x$ and $x^2$ are $3$ and $-6$. Find value of $m$ and $n$.

score 3.8k · Answer 1 · 2026-04-15 17:59:53

3.8k

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if in the expansion of $(1+x)^m (1-x)^n$, the coefficients of $x$ and $x^2$ are $3$ and $-6$. Find value of $m$ and $n$.

Published on 15 Apr 2026 - 17:59

score 255 · Answer 2 · 2026-04-14 12:12:44

255

Views

Prove that the free term of the polynomial $f (x)$ is equal to $f (0)$.

Published on 14 Apr 2026 - 12:12

score 81 · Answer 3 · 2026-04-16 12:34:16

81

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Roots of a cubic polynomial in $[-1,1]$

Published on 16 Apr 2026 - 12:34

score 97 · Answer 4 · 2026-04-16 14:50:42

97

Views

Let $K$ be a ring with unity. Prove that $K[X_1, \ldots, X_{m+1}]$ and $K[X_1, \ldots, X_{m}][X]$ are isomorphic

Published on 16 Apr 2026 - 14:50

score 471 · Answer 5 · 2026-04-14 21:56:48

471

Views

Prove that the sum of the coefficients of the polynomial $f(x)$ is equal to $f(1)$.

Published on 14 Apr 2026 - 21:56

score 53 · Answer 6 · 2026-04-16 19:52:20

53

Views

$P(x) = 1+x+x^2+x^3+x^4+x^5$ Then find remainder when $P(x^{12})$ is divided by $P(x)$

Published on 16 Apr 2026 - 19:52

score 65 · Answer 7 · 2026-04-15 06:03:34

65

Views

Factoring Polynomials into Galois Conjugate Linear Factors

Published on 15 Apr 2026 - 6:03

score 124 · Answer 8 · 2026-04-10 00:22:36

124

Views

How to solve an equation with 6 degree polynomial?

Published on 10 Apr 2026 - 0:22

score 119 · Answer 9 · 2026-04-16 05:46:52

119

Views

Proving $f(x)=x^4+4x^3+3x^2+7x-4$ is irreducible

Published on 16 Apr 2026 - 5:46

score 39 · Answer 10 · 2026-04-12 03:22:35

39

Views

Find all the values of parameter a, when system has 2 solutions.

Published on 12 Apr 2026 - 3:22

score 9.8k · Answer 11 · 2026-04-16 05:49:03

9.8k

Views

Compute polynomial $p(x)$ if $x^5=1,\, x\neq 1$ [reducing mod $\textit{simpler}$ multiples]

Published on 16 Apr 2026 - 5:49

score 2.3k · Answer 12 · 2026-04-13 15:24:23

2.3k

Views

Show $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$ (inverting unit + nilpotent)

Published on 13 Apr 2026 - 15:24

score 112 · Answer 13 · 2026-04-11 21:28:36

112

Views

Prove: Permutation of a root is another root of a polynomial

Published on 11 Apr 2026 - 21:28

score 414 · Answer 14 · 2026-04-11 04:21:13

414

Views

Every non-negative multivariate polynomial has even degree and the highest degree term has positive coefficient?

Published on 11 Apr 2026 - 4:21

score 366 · Answer 15 · 2026-04-12 02:53:47

366

Views

Irreducibily of polynomials in two variables

Published on 12 Apr 2026 - 2:53

List Question

if in the expansion of $(1+x)^m (1-x)^n$, the coefficients of $x$ and $x^2$ are $3$ and $-6$. Find value of $m$ and $n$.

Prove that the free term of the polynomial $f (x)$ is equal to $f (0)$.

Roots of a cubic polynomial in $[-1,1]$

Let $K$ be a ring with unity. Prove that $K[X_1, \ldots, X_{m+1}]$ and $K[X_1, \ldots, X_{m}][X]$ are isomorphic

Prove that the sum of the coefficients of the polynomial $f(x)$ is equal to $f(1)$.

$P(x) = 1+x+x^2+x^3+x^4+x^5$ Then find remainder when $P(x^{12})$ is divided by $P(x)$

Factoring Polynomials into Galois Conjugate Linear Factors

How to solve an equation with 6 degree polynomial?

Proving $f(x)=x^4+4x^3+3x^2+7x-4$ is irreducible

Find all the values of parameter a, when system has 2 solutions.

Compute polynomial $p(x)$ if $x^5=1,\, x\neq 1$ [reducing mod $\textit{simpler}$ multiples]

Show $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$ (inverting unit + nilpotent)

Prove: Permutation of a root is another root of a polynomial

Every non-negative multivariate polynomial has even degree and the highest degree term has positive coefficient?

Irreducibily of polynomials in two variables

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