The quadratic $x^2 + 12x + 35$ factors over the integers, because it can be written as $(x+r)(x+s)$ where $r$ and $s$ are integers. How many different quadratics in the form $x^2 + bx + 4b$ factor over the integers? One such quadratic is $x^2 + 3x + 12$, but it does not factor over the integers.