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I try to factor the polynomial t$^3$ $-$ 5t$^2$ $-$ 5t $-$ 1 = 0. But it cannot be done with rational root test obviously, plug in 1 and $-$1 does not work. Any other way to solve it quickly?

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  • $\begingroup$ Probably not..the roots are quite complicated. $\endgroup$ – Dzoooks Apr 24 at 1:38
  • $\begingroup$ A cubic with no rational root is irreducible over $\,\Bbb Q.\ \ $ $\endgroup$ – Bill Dubuque Apr 24 at 1:38
  • $\begingroup$ okay, thanks. by the way, if it is a characteristic equation for a matrix, does it mean we cannot obtain the eigenvalues? $\endgroup$ – Jonny Apr 24 at 1:40
  • $\begingroup$ The polynomial certainly has real roots, so the eigenvalues can be obtained. It's just that those real roots are not rational. $\endgroup$ – Greg Martin Apr 24 at 2:16
  • $\begingroup$ Is there any tricky way to do it? $\endgroup$ – Jonny Apr 24 at 5:12

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