If $f ( x ) = 4 x ^ { 2 } - 2 x - 7$, use synthetic division to evaluate $f \left( \frac { 7 } { 8 } \right)$.
A) $f \left( \frac { 7 } { 8 } \right) = \frac { 21 } { 2 }$
B) $f \left( \frac { 7 } { 8 } \right) = - \frac { 21 } { 2 }$
C) $f \left( \frac { 7 } { 8 } \right) = - \frac { 91 } { 16 }$
D) $f \left( \frac { 7 } { 8 } \right) = - \frac { 35 } { 2 }$
E) $f \left( \frac { 7 } { 8 } \right) = - \frac { 77 } { 8 }$

Question

Quizplus · Accepted Answer

To use synthetic division, we write the coefficients of the quadratic in the dividend and the root we want to evaluate in the divisor row:
$$
\begin{array}{c|cc c}
\frac{7}{8} & 4 & -2 & 0 & -7 \ \cline{2-5}
& & -\frac{1}{2} & \frac{1}{8} & \ 
\end{array}
$$
The bottom right corner is the remainder ($- \frac{91}{16}$), so $f \left( \frac { 7 } { 8 } \right) = - \frac { 91 } { 16 }$. Therefore, the correct answer is $\boxed{\textbf{(C)}}$.

If f(x)=4x2−2x−7f ( x ) = 4 x ^ { 2 } - 2 x - 7f(x)=4x2−2x−7

If $f ( x ) = 4 x ^ { 2 } - 2 x - 7$