Find the degree of the polynomial given: $2 - y^{2} - y^{3} + 2y^{8}$

Without actually calculating the cubes,find the value of each of the following: $(-12)^{3} + (7)^{3} + (5)^{3}$

Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = x^3 - 4x^2 + x + 6$,$g(x) = x - 3$.

Find the value of the polynomial $p(x) = 5x - 4x^2 + 3$ at $x = 2$.

Factorise: $27x^3 + y^3 + z^3 - 9xyz$

Verify whether the following is a zero of the polynomial indicated against it:
$p(x) = 2x + 1, \, x = \frac{1}{2}$