# 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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