<s>[INST] How can I factor the equation $a^3 - 5a^2 + 8a -4 = 0$? Consider the equality
$$
a^3 - 5a^2 + 8a -4 = 0
$$
What are the steps to factor this into the following?
$$
(a − 1)(a − 2)^2 = 0
$$
Is there some technique to do this?
 [/INST] \begin{align}
a^3 - 5a^2 + 8a -4 &= a^3 - a^2 -4a^2 + 8a -4 \\
                   &= a^2(a-1) - 4(a^2-2a+1) \\
                   &= a^2(a-1) - 4(a-1)^2\\
                   &= (a-1) \left[ a^2 - 4(a-1)\right] \\
                   &= (a-1)(a-2)^2
\end{align}
</s>