Roots,Roots Everywhere!

$x^{3}+8x^{2}+4x-11$
$Roots-\alpha,\beta,\gamma$
$By Vieta's Formula$
• $\alpha+\beta+\gamma=-8$
• $\alpha\beta\gamma=11$
• $\alpha\beta+\beta\gamma+\gamma\alpha=4$
$Another Polynomial$
$x^{3}+zx^{2}+fx+g$
$Roots-(\alpha + \beta$ ), ( $\alpha+ \gamma$ ,) ( $\beta+ \gamma$ )
$Again Vieta's Formula$
• $2(\alpha+\beta+\gamma)=-z$
$z=\boxed{16}$
• $(\alpha+\beta$ )× $(\alpha+\gamma$ )× $(\beta+\gamma$ ) $=-g$
$=$ $(-8-\gamma$ )× $(-8-\beta$ )× $(-8-\alpha$ )= $-g$
$g=\boxed{43}$
• $(\alpha+\beta$ ) $(\alpha+\gamma$ )+ $(\alpha+\gamma$ ) $(\beta+\gamma$ )+ $(\alpha+\beta$ ) $(\beta+\gamma$ ) $=f$
$=$ $\alpha^{2}+\beta^{2}+\gamma^{2}+3(\alpha \beta$ + $\alpha \gamma$ + $\beta \gamma$ )
$f=\boxed{68}$
$Now,$
$z×g×f=16×43×68=\boxed{46784}$