To find the remainder of the polynomial \( f(x) = 16x^2 - 20 \) when divided by \( x - \frac{3}{4} \), we can use the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial \( f(x) \) by \( x - c \) is equal to \( f(c) \).
In this case, \( c = \frac{3}{4} \).
Now, we will evaluate the polynomial \( f(x) \) at \( x = \frac{3}{4} \):
\[ f\left(\frac{3}{4}\right) = 16\left(\frac{3}{4}\right)^2 - 20 \]
Calculating \( \left(\frac{3}{4}\right)^2 \):
\[ \left(\frac{3}{4}\right)^2 = \frac{9}{16} \]
Now substitute this back into the polynomial:
\[ f\left(\frac{3}{4}\right) = 16 \cdot \frac{9}{16} - 20 \] \[ = 9 - 20 \] \[ = -11 \]
Therefore, the remainder when \( 16x^2 - 20 \) is divided by \( x - \frac{3}{4} \) is \( -11 \).
Thus, the correct answer is:
C \(-11\)
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