For how many ordered pairs (a, b) of integers does the polynomial x^{3}+a x^{2}+b x+6 have 3 distinct integer roots?

**Answer Choices**

A. 5

B. 6

C. 8

D. 7

E. 4

For how many ordered pairs (a, b) of integers does the polynomial x^{3}+a x^{2}+b x+6 have 3 distinct integer roots?

**Answer Choices**

A. 5

B. 6

C. 8

D. 7

E. 4