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\left(1-bc\right)a^{2}-a-6+9bc
Consider a^{2}-a-6-a^{2}bc+9bc as a polynomial over variable a.
\left(a-3\right)\left(-abc+a-3bc+2\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power \left(1-bc\right)a^{2} and n divides the constant factor 9bc-6. One such factor is a-3. Factor the polynomial by dividing it by this factor.