Use synthetic division and the Remainder Theorem to find the indicated function value.
-$$f ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 5 x ^ { 2 } + 8 x - 4 ; f \left( \frac { 1 } { 2 } \right)$$
A) $- \frac { 23 } { 16 }$
B) $- \frac { 23 } { 32 }$
C) $\frac { 23 } { 16 }$
D) $- \frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

To find $f\left(\frac{1}{2}\right)$ using synthetic division, we set up the division with $\frac{1}{2}$ as the divisor and the coefficients of $f(x)$ as the dividend: $1, -2, -5, 8, -4$. Performing synthetic division, we get a remainder of $-\frac{23}{16}$, which is the value of $f\left(\frac{1}{2}\right)$ according to the Remainder Theorem.

Use Synthetic Division and the Remainder Theorem to Find the Indicated