How do you find the imaginary roots of a fourth degree polynomial that cannot be simplified? I started out with $f(x)=16x^6-1$, and I got it down to $64x^4+16x^2+4$ by synthetically dividing by roots $0.5$ and $-0.5$ How should I continue in order to find the other roots?

Hint: \begin{align}64x^4 + 16 x^2 + 4 &= (8x^2-2)^2 + 32x^2 + 16x^2 
\\&= (8x^2-2)^2 + 48x^2
\\&= (8x^2-2)^2 - (4i\sqrt 3 x)^2
\end{align}
