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2x^{3}+7x^{2}+\frac{5}{2}x+3
Combine 4x and -\frac{3}{2}x to get \frac{5}{2}x.
\frac{4x^{3}+14x^{2}+8x-3x+6}{2}
Factor out \frac{1}{2}. Polynomial 4x^{3}+14x^{2}+5x+6 is not factored since it does not have any rational roots.