Find a zero of the polynomial $p(x) = 2x + 1$.

Write the following cube in expanded form: $(2a - 3b)^{3}$

Factorise $: 8 x^{3}+y^{3}+27 z^{3}-18 x y z$

Factorise : $x^{3}-3 x^{2}-9 x-5$

Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $x+\pi$.

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