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-2a^{2}+\left(3+4b\right)a-2b^{2}-3b
Consider 3a-2a^{2}-2b^{2}+4ab-3b as a polynomial over variable a.
\left(-a+b\right)\left(2a-2b-3\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power -2a^{2} and n divides the constant factor -2b^{2}-3b. One such factor is -a+b. Factor the polynomial by dividing it by this factor.