  We investigate all the four-body graviton interaction processes:
$gX\rightarrow \gamma X$, $gX\rightarrow gX$, and $gg\rightarrow gg$ with $X$
as an elementary particle of spin less than two in the context of linearized
gravity except the spin-3/2 case. We show explicitly that gravitational gauge
invariance and Lorentz invariance cause every four-body graviton scattering
amplitude to be factorized. We explore the implications of this factorization
property by investigating polarization effects through the covariant density
matrix formalism in each four-body graviton scattering process.
