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

$x+3$

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

$p(x)=x^{3}-3 x^{2}+4 x+50, g(x)=x-3$

Write the degree of each of the following polynomials

$x^{8}-6561$

On dividing $p(x)=x^{3}+2 x^{2}-5 a x-7$ by $(x+1),$ the remainder is $R _{1}$ and on dividing $q(x)=x^{3}+a x^{2}-12 x+6$ by $(x-2), \quad$ the remainder is $R _{2} .$ If $2 R _{1}+ R _{2}=6,$ then find the value of $a$.

Expand the following:

$\left(4-\frac{1}{3 x}\right)^{3}$

Factorise the following quadratic polynomials by splitting the middle term

$12 x^{2}+23 x+5$