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(2x-1)(2x+1)(2x+3)
Step-by-step explanation:
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 8. One such root is -\frac{3}{2}. Factor the polynomial by dividing it by 2x+3.
Consider 4x^{2}-1. Rewrite 4x^{2}-1 as \left(2x^2-1^2). The difference of squares can be factored using the rule: a^{2}-b^{2}.