For the factorising technique "adding zero" how am I supposed to know what "zero" to add?

Question

Let be $$x^4 - x^2 - 2x -1$$

I used photomath to see that $x^3$ needs to be added and subtracted. How would I have been able to figure this out myself?

Answer 1

It's $$x^4-(x+1)^2=(x^2-x-1)(x^2+x+1).$$