How to show $x^4 - 1296 = (x^3-6x^2+36x-216)(x+6)$ How to get this result: $x^4-1296 = (x^3-6x^2+36x-216)(x+6)$?
It is part of a question about finding limits at mooculus.

Here's a harder and similar way, but it still makes sense if you don't have what Julien said memorized. 
$$x^4 - 1296 = x^4 - 6^4 \Rightarrow x^4 = 6^4$$Now two roots that seem obvious are $6$ and $-6$. But $x^4 =  x^4 \cdot 1 = x^4 \cdot i^4 = (xi)^4$. So two more roots are $6i$ and $-6i$.
Hence, the factorization is $$\begin{aligned}&(x - 6)(x + 6)(x+6i)(x - 6i) \\  =& (x-6)(x+6)(x^2+36) \\ =& (x+6)(x^3 - 6x^2 +36x-216)\end{aligned}$$
