Show that $x-1$ is a factor of $P(x)$ where $P(x^5)+xQ(x^5)+x^2R(x^5)=\big(x^4+x^3+x^2+x+1\big)S(x)$
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
85287
Prove that, for $p > 3$, $(\frac 3p) = 1$ when $p \equiv 1,11 \pmod{12}$ and $(\frac 3p) = -1$ when $p \equiv 5,7 \pmod{12}$
95692
Factoring polynomials of the form $1+x+\cdots +x^{p-1}$ in finite field
10589
How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
85525
Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$
44878
Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
53725
Factor $(x+y)^4+x^4+y^4$
97652
Can every real polynomial be factored up to quadratic factors?
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
73277
Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
103803
Prove from first princibles $\frac{x^2-4}{x-4} \rightarrow -5$ as $x \rightarrow 3$
24864
$ \Big(\dfrac{x^7+y^7+z^7}{7}\Big)^2=\Big(\dfrac{x^5+y^5+z^5}{5}\Big)^2\cdot\Big(\dfrac{x^4+y^4+z^4}{2}\Big) $
121404
How to factor polynomials in $\mathbb{Z}_n$?
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$