Find the factors of $(a-b)^{3}+(b-c)^{3}+(c-a)^{3}$.

If $x=\sqrt{3}$,then the value of $x^{4}+2+\frac{1}{x^{4}}$ will be

When $4x^3 - ax^2 + bx - 4$ is divided by $x - 2$ and $x + 1$,the respective remainders are $20$ and $-13$. Find the values of $a$ and $b$.

When $(x^{3}-2 x^{2}+p x-q)$ is divided by $(x^{2}-2 x-3)$,the remainder is $(x-6)$. The values of $p$ and $q$ are:

Find the values of $m$ and $n$ in the polynomial $2x^{3} + mx^{2} + nx - 14$,such that $(x-1)$ and $(x+2)$ are its factors.

Divide the polynomial $4y^{3}-3y^{2}+2y-4$ by $y+2$ and find the quotient and remainder.