Final answer:
The correct factored form of the expression 2x^3 + 4x^2 + 6x + 12 is 2(x^3 + 2x^2 + 3x + 6), which corresponds to option A.
Step-by-step explanation:
To factor completely the expression 2x^3 + 4x^2 + 6x + 12, we first look for a common factor in all terms. In our case, this is the number 2. Factoring out the 2, we get:
2(x^3 + 2x^2 + 3x + 6)
After factoring out the 2, we need to check if the remaining trinomial can be factored further. However, the trinomial inside the parentheses does not factor neatly with real numbers, meaning it cannot be further factored into a product of binomials. Therefore, the completely factored form of our expression is:
2(x^3 + 2x^2 + 3x + 6).
Comparing this result with our multiple-choice options, we see that option A is the correct choice.