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