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\left(2j+1\right)\left(7j^{2}+6\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 6 and q divides the leading coefficient 14. One such root is -\frac{1}{2}. Factor the polynomial by dividing it by 2j+1. Polynomial 7j^{2}+6 is not factored since it does not have any rational roots.