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12\left(4x^{3}+5x^{4}+3x\right)
Factor out 12.
x\left(4x^{2}+5x^{3}+3\right)
Consider 4x^{3}+5x^{4}+3x. Factor out x.
12x\left(4x^{2}+5x^{3}+3\right)
Rewrite the complete factored expression. Polynomial 4x^{2}+5x^{3}+3 is not factored since it does not have any rational roots.