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3a^{2}-8ba+5b^{2}
Consider 3a^{2}-8ab+5b^{2} as a polynomial over variable a.
\left(3a-5b\right)\left(a-b\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 5b^{2}. One such factor is 3a-5b. Factor the polynomial by dividing it by this factor.