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To use the Distributive Property and factor the expression \( 4x^3 + 8x^2 + 12x \), we can first factor out the common factor, which is \( 4x \):
\[
4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3)
\]
Now, let's look at the options provided. The expression \( 4x(x^2 + 2x + 3) \) corresponds to the second choice:
**4x(x² + 2x + 3)**
Therefore, the correct answer is:
**4x(x² + 2x + 3)**.