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2\left(6x^{3}+x^{2}+3x\right)
Factor out 2.
x\left(6x^{2}+x+3\right)
Consider 6x^{3}+x^{2}+3x. Factor out x.
2x\left(6x^{2}+x+3\right)
Rewrite the complete factored expression. Polynomial 6x^{2}+x+3 is not factored since it does not have any rational roots.