Jimmy is trying to factor the quadratic equation $ax^2 + bx + c = 0.$ he assumes that it will factor in the form \[ax^2 + bx + c = (ax + b)(cx + d),\]where $a,$ $b,$ $c,$ and $d$ are integers. if $a = 4,$ and jimmy wants to find the value of $a,$ what are the possible values he should check, in order to find $a$?