Factor
\left(-y^{2}-1\right)\left(3a+2b-3ay^{2}\right)
Evaluate
3ay^{4}-2by^{2}-2b-3a
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\left(-2-2y^{2}\right)b-3a+3ay^{4}
Consider -3a-2b-2by^{2}+3ay^{4} as a polynomial over variable b.
\left(-y^{2}-1\right)\left(-3ay^{2}+2b+3a\right)
Find one factor of the form kb+m, where kb divides the monomial with the highest power \left(-2-2y^{2}\right)b and m divides the constant factor 3ay^{4}-3a. One such factor is -y^{2}-1. Factor the polynomial by dividing it by this factor. Polynomial -y^{2}-1 is not factored since it does not have any rational roots.
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