For a polynomial p(x), the value of p(3) is −2. which of the following must be true about p(x)? a) x−5 is a factor of p(x). b) x−2 is a factor of p(x). c) x+2 is a factor of p(x). d) the remainder when p(x) is divided by x−3 is −2.

This is the remainder factor theorem.

The theorem (I don't remember exactly) basically says something about how if you divide P(x) by (x+b), the remainder can be found by P(-b).

So in this case, since its p(3), this means that -b = 3
b = -3

So x+b = x-3.

That means p(x) is divided by x-3. There is a remainder of -2 when P(x) is divided by this. Therefore the last one is correct.

The rest cannot be correct as we have no information about them

Its probably the possible factors tt, tt, tt,