Unable to determine without specific values of a, b, c, and d and the correct option is C.
When a polynomial function f(x) is divided by a linear expression (x + a), the remainder is of the form bx + c, where b and c are constants. In this case, the remainder when f(x) = ax³ + ba² + cx + d is divided by (x + 2) is of the form bx + c.
The value of f(-2) can be calculated directly by substituting x = -2 into the expression for f(x):
f(-2) = a(-2)³ + b(-2)² + c(-2) + d = -8a + 4b - 2c + d
The remainder when f(x) is divided by (x + 2) is also calculated by substituting x = -2 into the expression for bx + c:
bx + c = b(-2) + c = -2b + c
Therefore, in order to determine whether f(-2) is greater than, equal to, or less than the remainder, we need to compare the expressions -8a + 4b - 2c + d and -2b + c.
However, without knowing the specific values of a, b, c, and d, it is impossible to determine which expression is larger. Therefore, the answer is **c. Unable to be determined**.