1979 AHSME Problem 25

If q_1 ( x ) and r_ 1 are the quotient and remainder, respectively, when the polynomial x^ 8 is divided by x + \tfrac{1}{2} , and if q_ 2 ( x ) and r_2 are the quotient and remainder, respectively, when q_ 1 ( x ) is divided by x + \tfrac{1}{2}, then r_2 equals

\textbf{(A) }\frac{1}{256}\qquad \textbf{(B) }-\frac{1}{16}\qquad \textbf{(C) }1\qquad \textbf{(D) }-16\qquad \textbf{(E) }256

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.