Are there other ways to factor polynomials, some sort of log function or recurrence relation?

I know that the most efficient way is with synthetic or long division, but It would make sense that there are other ways. I don't really care about how fast or well it work I am just curious.

  • $\begingroup$ How do you factor $2x^4-3x^3+x^2-x-2$ “with synthetic or long division”? $\endgroup$ – José Carlos Santos Sep 27 '17 at 14:45
  • $\begingroup$ Look up Diophantine Equations by Andreescu, Andrica, Cucurezeanu$$x^3-x^2+y^3-y^2=0 \ \ \ \implies$$ $$\left[3(x+y)-2\right]\cdot\left[9(x^2-xy+y^2)-3(x+y)-2\right]=4$$ $$x^2(y-1)+y^2(x-1)=1 \implies (x+y+2)(xy-x-y+2)=5$$ $\endgroup$ – AmateurMathPirate Sep 27 '17 at 16:28

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