The cubic polynomial $p\left( x \right)$ is defined by
$p\left( x \right) = 6{x^3} + \alpha {x^2} + bx + 10$,
where $\alpha $ and $b$ are constants. It is given that $\left( {x + 2} \right)$ is a factor of $p\left( x \right)$ and that, when $p\left( x \right)$ is divided by $\left( {x + 1} \right)$, the remainder is 24.
a) Find the values of $\alpha $ and $b$.
b) When $\alpha $ and $b$ have these values, factorise $p\left( x \right)$ completely.
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