What is the product of \( 3 x\left(x^{2}+4\right) \) ? \( x^{2}+3 x+4 \) \( 3 x^{3}+4 \) \( 3 x^{3}+12 x \) \( 3 x^{2}+12 x \)

To find the product of \( 3x(x^2 + 4) \), we need to distribute \( 3x \) across the terms inside the parentheses. First, multiply \( 3x \) by \( x^2 \), which gives \( 3x^3 \). Next, multiply \( 3x \) by \( 4 \), resulting in \( 12x \). So, putting it all together, we get \( 3x(x^2 + 4) = 3x^3 + 12x \). Therefore, the correct answer is \( 3x^3 + 12x \). If you chose or planned to choose that option, congratulations! You nailed it! For a little historical context, polynomial expressions like the one we dealt with here have roots back to ancient civilizations, including the Babylonians and Greeks, who laid the groundwork for algebra. The ability to manipulate these expressions has evolved significantly over centuries, leading to the advanced algebra we use today! If you’re ever diving into algebra, remember to take your time with distribution and keep an eye out for common mistakes like forgetting to apply the term across all components of the parentheses. It's easy to do, and double-checking your work can save you from minor slip-ups!