$\mathrm{lf} \mathrm{x}=2\mathrm{\omega }-1 \mathrm{then} {\mathrm{x}}^4+5{\mathrm{x}}^3+9{\mathrm{x}}^2-\mathrm{x}-14=$=

$\mathrm{x}=2\mathrm{\omega }-1\Rightarrow x^2=4{\omega }^2-4\omega +1$

$x^3=\left(4{\omega }^2-4\omega +1\right)\left(2\mathrm{\omega }-1\right)=8-4{\omega }^2-8{\omega }^2+4\omega +2\omega -1=7-12{\omega }^2+6\omega$

$$\begin{gathered} x^4=\left(7-12{\omega }^2+6\omega \right)\left(2\omega -1\right) \\ =14\omega -7-24+12{\omega }^2+12{\omega }^2-6\omega =24{\omega }^2+8\omega -31 \end{gathered}$$

$$\begin{gathered} {\mathrm{x}}^4+5{\mathrm{x}}^3+9{\mathrm{x}}^2-\mathrm{x}-14= \\ \left(24{\omega }^2+8\omega -31\right)+5\left(7-12{\omega }^2+6\omega \right)+9\left(4{\omega }^2-4\omega +1\right)-\left(2\omega -1\right)-14 \\ =0 \end{gathered}$$