x^2 + sx + 72 = 0 has two distinct integer roots; how many values are possible for s?
Choose the correct choice from the following choices:
A) 3 B) 6 C) 8 D) 12 E) 24

Rationale: for a quadratic equation ax ^ 2 + sx + c = 0 , we know that - s / a is sum of roots and c / a is product of roots . the quadratic equation here is x ^ 2 + sx + 72 = 0 , where product of roots is 72 . if we find all the factors of 72 , we have the answer . by prime factorization , we get 72 = 2 ^ 3 * 3 ^ 2 . we know that total factors are ( 3 + 1 ) * ( 2 + 1 ) = 12 ( reason : with 2 ^ n , we have n + 1 possibilities . n ^ 0 to n ^ n . so n + 1 ) = d
Answer: D