Answer
$b=0,3,4,-k(k+4)$
Work Step by Step
Step 1. Given $x^2+bx+15$, we need to find all the possibilities of two number giving a sum of $4$; we have
$0+4, 1+3, -1+5, 2+2, -2+6, -3+7, ... -k+(k+4), k\gt0$
Step 2. The value of $b$ is the product of the two numbers; thus we have $b=0,3,4,-k(k+4)$ (where the integer $k\gt0$) as possible values.
