The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?
Simplify as
x^2 -mx + 14 = 0
Note that the possible factorizations are
( x - 7) (x - 2) m = 9
( x + 7) (x + 2) m = -9
(x - 14) ( x -1) m = 14
(x + 14) ( x + 1) m = -14
+354 
