Answer
$\displaystyle \frac{49}{64}$
Work Step by Step
Remainder Theorem:
If the polynomial $P(x)$ is divided by $x-c$ , then the remainder is the value $P(c)$ .
Important: zeros for missing powers of P(x).
$\left.\begin{array}{l}
\displaystyle \frac{1}{4} \ \lfloor \\ \\ \\ \\ \end{array}\right.\begin{array}{rrrrr}
1 & 0 & -1 & 1 \\\hline
& \displaystyle \frac{1}{4} & \displaystyle \frac{1}{16} & - \displaystyle \frac{15}{64} \\\hline
1 & \displaystyle \frac{1}{4} & - \displaystyle \frac{15}{16} &|\displaystyle \ \ \ \frac{49}{64} \end{array}$
$R(x)=P(\displaystyle \frac{1}{4})=\frac{49}{64}$
