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

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) $f \left( \frac { 7 } { 8 } \right) = - \frac { 77 } { 8 }$

Quizplus · Accepted Answer

We can use synthetic division as follows:
$$
\begin{array}{c|ccccc}
\frac{7}{8} & 4 & -2 & 0 & -7 \
\hline
& & 3 & \frac{1}{4} & \frac{1}{8} \
\hline
4 & 1 & \frac{1}{2} & \frac{1}{4} & -\frac{55}{64}
\end{array}
$$
Therefore, $f \left( \frac{7}{8} \right) = -\frac{55}{64}$. Simplifying this gives $f \left( \frac{7}{8} \right) = -\frac{91}{16}$. Therefore, the answer is C.

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

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