The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - c \), the remainder of this division is equal to \( f(c) \).
In your case, since \( f(x) = x^4 - 5x^3 + 8x \) is divided by \( x - 3 \) and the remainder is -30, we have:
\[ f(3) = -30 \]
Now let's examine the options:
A. \( f(-3) = 30 \) - This is not supported by the Remainder Theorem regarding \( x - 3 \).
B. \( f(-3) = -30 \) - We don't have information about \( f(-3) \) related to the division by \( x - 3 \).
C. \( f(3) = -30 \) - This is correct as per our findings.
D. \( f(3) = 30 \) - This contradicts our result \( f(3) = -30 \).
The only correct statement according to the Remainder Theorem in this case is:
C. f(3) = -30.