To apply the Remainder Theorem, we need to evaluate the function \( f(x) = 9x^2 - 50 \) at \( x = 73 \). The Remainder Theorem states that the remainder of dividing a polynomial \( f(x) \) by \( x - c \) is equal to \( f(c) \).
Here, \( c = 73 \).
Now, let's calculate \( f(73) \):
\[ f(73) = 9(73)^2 - 50 \]
First, calculate \( 73^2 \):
\[ 73^2 = 5329 \]
Now, substitute back into the function:
\[ f(73) = 9(5329) - 50 \]
Calculating \( 9 \times 5329 \):
\[ 9 \times 5329 = 47961 \]
Now, subtract 50:
\[ f(73) = 47961 - 50 = 47911 \]
Thus, the remainder when \( 9x^2 - 50 \) is divided by \( x - 73 \) is:
\[ \boxed{47911} \]
Since none of the answer options provided appear to align with the calculated result, it seems that there may have been a misunderstanding or misprint in the choices given.
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