1951 AHSME Problem 18

The expression 21x^2+ax+21 is to be factored into prime binomial factors and without a numerical monomial factor. This can be done if the value ascribed to a is:

\textbf{(A)}\ \text{any odd number}\qquad\textbf{(B)}\ \text{some odd number}\qquad\textbf{(C)}\ \text{any even number}\qquad\textbf{(D)}\ \text{some even number}\qquad\textbf{(E)}\ \text{zero}

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