Final answer:
The polynomial 2x^5 + 12x^3 - 54x is completely factored as 2x(x^2 - 3)(x^2 + 9), by factoring out the greatest common factor and recognizing the difference of squares.
Step-by-step explanation:
The completely factored form of the polynomial 2x^5 + 12x^3 - 54x can be found by first factoring out the greatest common factor (GCF), which is 2x. After factoring out the GCF, the polynomial becomes 2x(x^4 + 6x^2 - 27). The quadratic part can be factored further as it is a difference of squares, resulting in the factors (x^2 - 3)(x^2 + 9). Therefore, the completely factored form of the polynomial is D. 2x (x^2 - 3)(x^2 + 9).