factoring a polynomial which cannot be done with rational root test.

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?

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