Final answer:
The polynomial 2x³ + 5x² + 6x + 15 can be factored by grouping, resulting in the factored form (2x + 5)(x² + 3).
Step-by-step explanation:
To factor the polynomial expression 2x³ + 5x² + 6x + 15, we must look for common patterns or use methods such as grouping. Let's attempt to factor by grouping:
- Group terms with common factors: (2x³ + 5x²) + (6x + 15)
- Factor out the greatest common factor from each group: x²(2x + 5) + 3(2x + 5)
- Notice that (2x + 5) is a common factor: (2x + 5)(x² + 3)
Therefore, the factored form of the expression is (2x + 5)(x² + 3).