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25a^{2}+\left(10x-10\right)a+x^{2}-2x
Consider 25a^{2}+x^{2}+10ax-10a-2x as a polynomial over variable a.
\left(x+5a\right)\left(x+5a-2\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 25a^{2} and n divides the constant factor x^{2}-2x. One such factor is x+5a. Factor the polynomial by dividing it by this factor.