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 \(\eta+\delta\).


Bonus: Find the other factor of \(\zeta(\gamma)\).

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