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x^{2}-10yx-171y^{2}
Consider x^{2}-10xy-171y^{2} as a polynomial over variable x.
\left(x-19y\right)\left(x+9y\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 -171y^{2}. One such factor is x-19y. Factor the polynomial by dividing it by this factor.