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15x^{2}+\left(2y-z\right)x-24y^{2}-6z^{2}+24yz
Consider 15x^{2}-24y^{2}-6z^{2}+2xy-xz+24yz as a polynomial over variable x.
\left(3x+4y-2z\right)\left(5x-6y+3z\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 15x^{2} and n divides the constant factor -24y^{2}+24yz-6z^{2}. One such factor is 3x+4y-2z. Factor the polynomial by dividing it by this factor.