Will factor theorem help here?

Algebra Level 4

$\large\zeta(\gamma) = \eta\gamma^4+\delta\gamma^3+32\gamma^2-17\gamma + 6$

Above shows a 4th degree polynomial $\zeta(\gamma)$ with constant leading term $\eta$ . If $(3\gamma^2-2\gamma+1)$ divides the polynomial $\zeta(\gamma)$ , find the value of $\eta+\delta$ .