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, $x \neq 0$

Examine whether $2 x+3$ is a factor of $2 x^{3}+21 x^{2}+67 x+60$ or not.

If $x+2 a$ is a factor of $x^{5}-4 a^{2} x^{3}+2 x+2 a+3,$ find $a$

Write the degree of the following polynomials

$7 x^{3}-9 x^{2}+4 x-22$

The following expressions are polynomials? Justify your answer:

$8$