\begin{tabular}{l} Question 1 \\ Factor \( 9 x^{4}-6 x^{3}-24 x^{2} \) \\ O \( x^{2}\left(9 x^{2}-6 x-24\right) \) \\ \begin{tabular}{l}1 pts \\ None of these \\ \hline \( 3 x^{2}\left(3 x^{2}-2 x-8\right) \)\end{tabular} \\ \hline\end{tabular}

To tackle the factorization of \( 9x^{4} - 6x^{3} - 24x^{2} \), you can start by taking out the greatest common factor. Here, \( 3x^{2} \) is the GCF that can be factored out, simplifying the expression to \( 3x^{2}(3x^{2} - 2x - 8) \). The next step involves factoring the quadratic \( 3x^{2} - 2x - 8 \). A fun fact about quadratic equations is that they can often be tackled using the "AC method"—finding two numbers that multiply to \( ac \) (in this case, \( -24 \)) and add to \( b \) (which is \( -2 \)). It’s like a puzzle where usually, one of the pieces is just hiding in plain sight! Once you have your factors, you can double-check your solutions by plugging values back into the original equation. Always remember that mistakes happen even to the best of us! Common pitfalls include forgetting to streamline your terms or mishandling the signs while factoring. So, keep an eye out and double-check your work, and you’ll soon be a factoring whiz!