The polynomial $p(x)$ is defined as $p(x) = 4x^3 + ax^2 + ax + 4$, with $a$ a constant.
(i)[2]
Use the factor theorem to show that $(x + 1)$ is a factor of $p(x)$ for every value of $a$.
(ii)[2]
Since the remainder is $-42$ when $p(x)$ is divided by $(x - 2)$, find the value of $a$.
(iii)[4]
When $a$ takes the value found in part (ii), factorise $p(x^2)$ completely.
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