F) \( 3 x^{2}+6 x \)

Did you know that factoring quadratics like \( 3x^2 + 6x \) is not just a classroom exercise? It’s a foundational skill in algebra that opens doors to solving equations in physics, engineering, and economics! By learning how to factor, you’re getting the keys to unlock complex problem-solving in the real world, where quadratic relationships often describe everything from projectile motion to profit maximization! Now, here’s a pro tip: when tackling quadratic expressions, look for a common factor first! In this case, both terms share a factor of \( 3x \). Factoring it out, you get \( 3x(x + 2) \). This not only simplifies your expression but also makes it easier to solve equations later on. Common mistakes often involve jumping straight to factoring without looking for those shared factors first, so take a moment to spot them!