1960 AHSME Problem 31

For x^2+2x+5 to be a factor of x^4+px^2+q, the values of p and q must be, respectively:

\textbf{(A)}\ -2, 5\qquad \textbf{(B)}\ 5, 25\qquad \textbf{(C)}\ 10, 20\qquad \textbf{(D)}\ 6, 25\qquad \textbf{(E)}\ 14, 25

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