# Recent questions tagged polynomials

1
Find all the polynomials with real coefficients $P\left(x \right)$ such that $P\left(x^{2}+x+1 \right)$ divides $P\left(x^{3}-1 \right)$. $ax^{n}$ $ax^{n+2}$ $ax$ $2ax$
2
The roots of the equation $x^{2/3}+x^{1/3}-2=0$ are : $1, -8$ $-1, -2$ $\frac{2}{3}, \frac{1}{3}$ $-2, -7$
1 vote
3
If $x^{a}=y^{b}=z^{c}$ and $y^{2}=zx$ then the value of $\frac{1}{a} + \frac{1}{c}$ is : $\frac{b}{2}$ $\frac{c}{2}$ $\frac{2}{b}$ $\frac{2}{a}$
4
$\left [\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}} \right ]$ equal to : $1$ $0$ $\frac{8}{1-x^{8}}$ $\frac{16}{1-x^{16}}$
1 vote
If $t^{2}-4t+1=0$, then the value of $\left[t^{3}+1/t^{3} \right]$ is : $44$ $48$ $52$ $64$
If $a^{x}=b$, $b^{y}=c$ and $c^{z}=a$, then the value of $xyz$ is : $0$ $1$ $\frac{1}{3}$ $\frac{1}{2}$
Let $S$ denote the infinite sum $2+5x+9x^{2}+14x^{3}+20x^{4}+\ldots$ where $\mid x \mid < 1$ and the coefficient of $x^{n-1}$ is $\dfrac{1}{2}n\left ( n+3 \right ), \left ( n=1,2,\ldots \right ).$ Then $S$ equals $\frac{2-x}{(1-x)^{3}}$ $\frac{2-x}{(1+x)^{3}}$ $\frac{2+x}{(1-x)^{3}}$ $\frac{2+x}{(1+x)^{3}}$