Answers are: A, B, and D
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A more detailed breakdown:
A) True because we have a remainder of 0, which is the last value in the bottom row.
B) True because of the same basic reasoning as choice A above
C) False. x+2 is not a factor since x-2 is instead. The two factors are (x-2) and (3x-5)
D) True. Similar reasoning to A and B above. If x-2 is a factor, then x-2 = 0 leads to x = 2 being a root. So f(2) = 0
E) False. This is in line with what I'm saying in choice C above
F) False. Since x+2 is not a factor, this means x+2 = 0 ---> x = -2 is not a root.