If the polynomials $a z^{3}+4 z^{2}+3 z-4$ and $z^{3}-4 z+a$ leave the same remainder when divided by $z-3,$ find the value of $a$.

Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by

$x-2$

Find the zero of the polynomial in each of the following cases

$q(m)=0.3 m-0.15$

Factorise

$12 x^{3}+17 x^{2}+3 x-2$

If $(5 x-3)^{2}=25 x^{2}+k x+9,$ then find $k$

By remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where

$p(x)=x^{3}-6 x^{2}+2 x-4, \quad g(x)=1-\frac{3}{2} x$