Will factor theorem help here?

Algebra Level 4

ζ(γ)=ηγ4+δγ3+32γ217γ+6\large\zeta(\gamma) = \eta\gamma^4+\delta\gamma^3+32\gamma^2-17\gamma + 6

Above shows a 4th degree polynomial ζ(γ)\zeta(\gamma) with constant leading term η \eta. If (3γ22γ+1)(3\gamma^2-2\gamma+1) divides the polynomial ζ(γ) \zeta(\gamma), find the value of η+δ\eta+\delta.


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

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