$$1+4x+4x^{2}-16x^{4}$$
$-16x^{4}+\left(2x+1\right)^{2}$
$-4\left(x-\frac{1-\sqrt{5}}{4}\right)\left(x-\frac{\sqrt{5}+1}{4}\right)\left(4x^{2}+2x+1\right)$
