(i)[2]
The polynomial $f(x)$ can be expressed in the form $(x - 2)^2 g(x)$, where $g(x)$ is another polynomial. Show that $(x - 2)$ is a factor of $f'(x)$.
(ii)[5]
The polynomial $x^5 + ax^4 + 3x^3 + bx^2 + a$, where $a$ and $b$ are constants, has $(x - 2)^2$ as a factor. Using the factor theorem and the result of part (i), or otherwise, find the values of $a$ and $b$.