# Factoring a polynomial of degree 4

I am attempting to factor a relatively benign looking polynomial of degree 4. I have tried to use synthetic division to factor this. I was hoping to be able to get a remainder of zero at some point. I don't quite know how this works but I suspect that if perhaps I extend things to complex numbers I might have some luck. For this same reason, I am suspecting that all of the roots are may be complex. Can someone tell me how one deals with this?

• I indeed ran across that link, and was considering depressing the quartic or something. In fact just to confirm I am pursuing the correct avenues, a specific case of the polynomial in question is $$(2t^4 - 6 t^3 + 3 t^2 - 12 t -3)$$ – user543213 Mar 19 '18 at 2:14