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