Recent questions tagged polynomials

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$

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$

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}$

$\left [\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}} \right ]$ equal to :$1$$0$$\frac{8}{1-x^{8}}$$\frac{16}{1-x^{16}}$

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}$