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x^{2}+\left(8-3y\right)x+16-12y
Consider x^{2}+8x+16-3xy-12y as a polynomial over variable x.
\left(x+4\right)\left(x-3y+4\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 -12y+16. One such factor is x+4. Factor the polynomial by dividing it by this factor.