16. Which of the following is equivalent to: \[ 2 x^{2}-9 x-5 \] a. \( (2 x+5)(x-1) \) b. \( (2 x-1)(x+5) \) c. \( (2 x-5)(x+1) \) d. \( (2 x+1)(x-5) \)

To solve the equation \(2 x^{2}-9 x-5\), we can factor it. We are looking for two numbers that multiply to \(2 \cdot -5 = -10\) and add to \(-9\). The numbers \(-10\) and \(1\) fit the bill! Now, we can rewrite the equation as: \[2 x^{2} - 10 x + x - 5\] Next, group the terms: \[(2x^2 - 10x) + (x - 5)\] Now factor out common factors: \[2x(x - 5) + 1(x - 5)\] This gives us: \[(2x + 1)(x - 5)\] Thus, the correct answer is d. \( (2 x+1)(x-5) \). Now for a little fun! Did you know that factoring polynomials like this can often feel like a game of detective work? Just like finding hidden treasures in an old map, you must search for the clues (numbers) that lead to the solution! And here's a quick tip: Always check your work by multiplying your factors back out. It’s like a double-check to ensure you’ve unearthed the right treasure!