Factorise the following quadratic polynomials by splitting the middle term

$x^{2}+10 x+16$

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

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

Check whether $g(x)$ is a factor of $p(x)$ or not, where

$p(x)=8 x^{3}-6 x^{2}-4 x+3, \quad g(x)=\frac{x}{3}-\frac{1}{4}$

Factorise $x^{2}-7 x+12$ by using the factor theorem.

If $a+b+c=5$ and $a b+b c+c a=10,$ then prove that $a^{3}+b^{3}+c^{3}-3 a b c=-25.$