How do you factor x^3 + x + 1?

This person at https://socratic.org/questions/how-do-you-factor-x-3-2x-1 did something similar apparently, but I could only follow up to x (x+1) (x-1) - (x+ 1), as the step immediately after that solves to x^3-1, not the x^3 + 2x -1 attempted there.
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