I've tried factoring as best as I can, I've tried to apply what little I can understand about the rational roots theorem. I've tried grouping. All to no avail. I think it must be a tricky one.

Function is.

$\displaystyle

f(x)=x^4+8x^3+6x^2-18x-10

$

Thoughts? Any obvious giveaways I'm overlooking? Root at

$\displaystyle \sqrt{2}$

$\displaystyle \sqrt{-2}$?