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4\left(3x^{4}yz^{2}-2x^{3}y^{3}z^{2}\right)
Factor out 4.
x^{3}yz^{2}\left(3x-2y^{2}\right)
Consider 3x^{4}yz^{2}-2x^{3}y^{3}z^{2}. Factor out x^{3}yz^{2}.
4x^{3}yz^{2}\left(3x-2y^{2}\right)
Rewrite the complete factored expression.