a) The polynomial ${x^4} + \alpha {x^3} - {x^2} + bx + 2$, where $\alpha $ and $b$ are constants, is denoted by $p\left( x \right)$. It is given that $\left( {x - 1} \right)$ and $\left( {x + 2} \right)$ are factors of $p\left( x \right)$. Find the values of $\alpha $ and $b$.
b) When $\alpha $ and $b$ have these values, find the quotient when $p\left( x \right)$ is divided by ${x^2} + x - 2$.
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