Evaluate the following products without multiplying directly

$76 \times 82$

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

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

Write whether the following statements are True or False. Justify your answer.

$\frac{1}{\sqrt{5}} x^{\frac{1}{2}}+1$ is a polynomial

If $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$

Factorise the following:

$25 x^{2}+16 y^{2}+4 z^{2}-40 x y+16 y z-20 x z$

With the help of the remainder theorem, find the remainder when the polynomial $x^{3}+x^{2}-26 x+24$ is divided by each of the following divisors

$x-1$