Find the value of the polynomial $x^{2}-7 x+12$ at.

$x=\frac{1}{2}$

Show that $p-1$ is a factor of $p^{10}-1$ and also of $p^{11}-1$

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

$p(x)=4 x^{3}-12 x^{2}+14 x-3, g(x)=2 x-1$

Show that :

$x+3$ is a factor of $69+11 x-x^{2}+x^{3}$.

For the polynomial $p(x),$ if $p(7)=0,$ then $\ldots$ is………… a factor of $p(x) .$