If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. ab + b^2
II. (a + b)^2
III. a + b Choose the correct choice:
A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III
Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.   I. ab + b^2 --&gt; if a=1 and b=2 then ab + b^2=6, which is a factor of 30. OK;   II. (a + b)^2 --&gt; (a + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;   III. a + b --&gt; if a=1 and b=2 then a + b=3, which is a factor of 30. OK.   Answer: II only.
<result>B</result>
If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. ab + b^2
II. (a + b)^2
III. a + b