Which shows one way to determine the factors of x³ + 9x² + 5x + 45 by grouping?

To factor the polynomial x³ + 9x² + 5x + 45 by grouping, we can follow these steps:

1. First, we group the terms in pairs: (x³ + 9x²) + (5x + 45).
2. Next, we factor out the greatest common factor from each group:
• From the first group x³ + 9x², we factor out x², giving us x²(x + 9).
• From the second group 5x + 45, we factor out 5, resulting in 5(x + 9).
3. This gives us: x²(x + 9) + 5(x + 9).
4. Now we notice that (x + 9) is a common factor in both terms, so we can factor it out:
• This simplifies to (x + 9)(x² + 5).

So, the final factored form of the polynomial x³ + 9x² + 5x + 45 is (x + 9)(x² + 5).