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3a^{2}+\left(-5b-1\right)a+2b^{2}-b-10
Consider 3a^{2}-5ab+2b^{2}-a-b-10 as a polynomial over variable a.
\left(3a-2b+5\right)\left(a-b-2\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 3a^{2} and n divides the constant factor 2b^{2}-b-10. One such factor is 3a-2b+5. Factor the polynomial by dividing it by this factor.