To do this, note that the quartic will be factorable if it can be written as the difference of two squared terms,

It turns out that a factorization of this form can be obtained by adding and subtracting x²u + u²/4 (where u is for now an arbitrary quantity, but which will be specified shortly) to the reduced quartic to obtain

This equation can be rewritten

Note that the first term is immediately a perfect square P² with

The second term will be a perfect square Q² if u is chosen to that the square can be completed in

This means

which requires that

or