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.

$$\begin{array}{r|rrrr|r}
& 1 & 0 & 0 & 0 & -1296 \\
-6 & & -6 & 36 & -216 & 1296 \\
\hline
& 1 & -6 & 36 & -216 & 0
\end{array}
$$
This shows that
$$
x^4-1296=(x+6)(x^3-6x^2+36x-216)
$$
Of course you can also use
$$
a^4 - b^4 = (a-b)(a^3 + a^2b + ab^2 + b^3)
$$
with $a=x$ and $b=-6$.
