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\left(x+1\right)\left(6x^{5}-6x^{4}+5x^{3}-5x^{2}+5x-3\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -3 and q divides the leading coefficient 6. One such root is -1. Factor the polynomial by dividing it by x+1. Polynomial 6x^{5}-6x^{4}+5x^{3}-5x^{2}+5x-3 is not factored since it does not have any rational roots.