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 $a$.

From the following polynomials find out which of them has $(x-1)$ as a factor

$2 x^{3}+5 x^{2}-x-6$

Evaluate the following using suitable identities

$(105)^{3}$

If $p(x)=x^{2}-4 x+3$ then, find the value of $p(2)-p(-1)+p\left(\frac{1}{2}\right)$

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

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