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\left(3q+1\right)\left(16q^{2}-15\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -15 and q divides the leading coefficient 48. One such root is -\frac{1}{3}. Factor the polynomial by dividing it by 3q+1. Polynomial 16q^{2}-15 is not factored since it does not have any rational roots.