Evaluate

$77 \times 83$

Factorise

$x^{2}+\frac{y^{2}}{4}+\frac{z^{2}}{16}+x y+\frac{y z}{4}+\frac{z x}{2}$

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

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

The following expressions are polynomials? Justify your answer:

$\frac{1}{x+1}$

Find the zeroes of the polynomial in each of the following:

$h(y)=2 y$

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

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