x^2 + hx + 72 = 0 has two distinct integer roots; how many values are possible for h?	Choose the most appropriate option
A) 3	B) 6	C) 8	D) 12	E) 24
For a quadratic equation ax^2+hx+c=0, we know that -h/a is sum of roots and c/a is product of roots.   The quadratic equation here is x^2 + hx + 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)= 
<gadget id="calculator"> (3+1)*(2+1)</gadget>
<output>12</output>
12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=12
<result>D</result>
x^2 + hx + 72 = 0 has two distinct integer roots; how many values are possible for h?