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\left(2x+1\right)\left(x^{2}-3x+4\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 4 and q divides the leading coefficient 2. One such root is -\frac{1}{2}. Factor the polynomial by dividing it by 2x+1. Polynomial x^{2}-3x+4 is not factored since it does not have any rational roots.