What would be the approach towards factoring $x^3 -8$ as $(x-2) \cdot (x^2+2x+4)$? I am not sure I would have been able to readily factor this without seeing the answer. How would one come about this factorization?
2026-04-04 23:01:34.1775343694
How to see that $x^3 -8$ can be factored as $(x-2) \cdot (x^2+2x+4)$?
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Observe that $2$ is an obvious root. The root-factor theorem then tells you that $x-2$ is a factor. Now just do polynomial division to divide $x^3-8$ by $x-2$. (If you were ever taught synthetic division, that is a “shortcut” accomplishing the same thing.)