For polynomial $p(x) = x^{3} - 3x^{2} + 8x + 12$,find the value of $p(-1)$.

Which of the following expressions is a polynomial? State the reason. If an expression is a polynomial,state whether it is a polynomial in one variable or not.
$5x^2 + 11x - 2\sqrt{x}$

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 6x^{2} + 2x - 4$ and $g(x) = 1 - \frac{3}{2}x$.

Is the following expression a polynomial? Justify your answer:
$\sqrt{3} x^{2}-2 x$

Write the degree of the following polynomial:
$7 x^{3}-9 x^{2}+4 x-22$

Classify the following as a constant,linear,quadratic,or cubic polynomial:
$y^{3}-y$