Without actually calculating the cubes, find the value of each of the following

$\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}$

If the polynomials $a z^{3}+4 z^{2}+3 z-4$ and $z^{3}-4 z+a$ leave the same remainder when divided by $z-3,$ find the value of $a$.

Write the degree of the following polynomials

$5$

Factorise the following quadratic polynomials by splitting the middle term

$x^{2}-12 x+20$

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

$\frac{6 \sqrt{x}+x^{\frac{3}{2}}}{\sqrt{x}}$ is a polynomial, $x \neq 0$