What is the remainder when $x^7-12x^5+23x-132$ is divided by $2x-1$? (Hint: Long division need not be used. What is the remainder when $x^7-12x^5+23x-132$ is divided by $2x-1$? (Hint: Long division need not be used.)
The Hint is confusing! 

You can use Horner schema to evaluate it. For an explanation of this algorithm read this. In your case you have
\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline &1&0&-12&0&0&0&23&-132 \\\hline\frac12 &0&\frac12&\frac14&-\frac{47}{8}&-\frac{47}{16}&-\frac{47}{32}&-\frac{47}{64}&\frac{1425}{128}\\\hline &1&\frac12&-\frac{47}{4}&-\frac{47}{8}&-\frac{47}{16}&-\frac{47}{32}&\frac{1425}{64}&\color{red}{-\frac{15471}{128}}\\\hline\end{array}
which, by the way, uses the same idea of the other answers, but it avoids you many calculation with high powers.
