1. The problem is to factor the polynomial expression $2x^3 - 6x$ by factoring out the common factor. 2. The formula used is factoring out the greatest common factor (GCF): $$a b + a c = a(b + c)$$ where $a$ is the GCF. 3. Identify the GCF of the terms $2x^3$ and $-6x$. The coefficients 2 and 6 have GCF 2, and the variable part $x^3$ and $x$ have GCF $x$. 4. Factor out the GCF $2x$: $$2x^3 - 6x = 2x(x^2 - 3)$$ 5. This is the completely factored form since $x^2 - 3$ cannot be factored further over the real numbers. Final answer: $$2x(x^2 - 3)$$