If integers d and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. db + b^2
II. (d + b)^2
III. d + b
Pick one:
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. db + b^2 --&gt; if d=1 and b=2 then db + b^2=6, which is a factor of 30. OK;   II. (d + b)^2 --&gt; (d + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;   III. d + b --&gt; if d=1 and b=2 then d + b=3, which is a factor of 30. OK.   Answer: II only.
<result>B</result>
If integers d and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. db + b^2
II. (d + b)^2
III. d + b