If $\alpha$, $\beta$, $\gamma$ are the zeroes of the cubic polynomial $p\left(x\right)=7x^3-21x^2+24x+5$ then find the value of ${\alpha }^{-1}+{\beta }^{-1}+{\gamma }^{-1}$.

Divide $p\left(x\right)$ by $g\left(x\right)$ in the following and write quotient and remainder.

$p\left(x\right)=x^3-3x^2+5x-3$

$g\left(x\right)=x^2-2$

Divide $p\left(x\right)$ by $g\left(x\right)$ in the following and write quotient and remainder.

$p\left(x\right)=x^4+2x^3-2x^2-2x-1$, $g\left(x\right)=x^2+2x-3$.

Check whether the first polynomial is a factor of the second polynomial by applying Euclid's division algorithm for the following:

$x^2+3x+1$, $3x^4+5x^3-7x^2+2x+2$

Check whether the first polynomial is a factor of the second polynomial by applying Euclid's division algorithm for the following:

$x^2-5x+6$, $10x^4+8x^2+6x+3$

Divide $6x^3+11x^2-39x-65$ by $x^2+x-1$ and hence verify division algorithm for the polynomials.