Final answer:
The original expression 2x³ + 5x² + 6x + 15 is equivalent to option A: (x + 3)(2x² + 5), as expanding this option results in the original expression.
Step-by-step explanation:
To find which expression is equivalent to 2x³ + 5x² + 6x + 15, we can attempt to factor by grouping or look for patterns that match the given options. Firstly, we notice that the expression does not factor neatly by grouping, and each term does not share a common factor other than 1, making it necessary to compare the provided options by expanding them.
Option A ((x + 3)(2x² + 5)) expands to 2x³ + 5x² + 6x + 15, matching the original expression. Option B would yield 2x³ + 3x² + 10x + 15, option C would result in 2x³ + 11x² + 15x + 15, and option D would give 2x³ + 13x² + 15x + 15. None of these match the original expression except for option A.
Thus, the equivalent expression is option A: (x + 3)(2x² + 5).