Final answer:
The LCM of the expressions 2a^2 + 5a + 2 and 2a^2 - 3a - 2 is d) (2a - 1)(a + 2).
Step-by-step explanation:
To find the LCM (Least Common Multiple) of the expressions 2a^2 + 5a + 2 and 2a^2 - 3a - 2, we need to factorize both expressions.
The factored form of the first expression is (2a + 1)(a + 2). The factored form of the second expression is (2a - 1)(a + 2).
The LCM is the product of the highest powers of each unique factor. In this case, the highest power of (2a + 1) is 1, the highest power of (2a - 1) is 1, and the highest power of (a + 2) is 1. Therefore, the LCM is (2a + 1)(2a - 1)(a + 2), which corresponds to option d) (2a - 1)(a + 2).