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2\left(xy^{2}+3x\right)
Factor out 2.
x\left(y^{2}+3\right)
Consider xy^{2}+3x. Factor out x.
2x\left(y^{2}+3\right)
Rewrite the complete factored expression. Polynomial y^{2}+3 is not factored since it does not have any rational roots.