Write the coefficient of $x^{2}$ in the following polynomial: $x^{3} + 27$.

Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}-12x+20$

Classify the following polynomial as a polynomial in one variable,two variables,etc.
$x^{2}+x+1$

By using the factor theorem,show that $(x-3)$ is a factor of the polynomial $p(x) = 12x^3 - 31x^2 - 18x + 9$ and then factorise the polynomial.

Classify the following polynomial as a polynomial in one variable,two variables,etc.
$y^{3}-5y$

If $x+2$ is a factor of $x^{3}+ax^{2}-x+30$,find the value of $a$.