For a polynomial p of x, the value of p of three is minus two, which of the following must be true about p of x? It must be true is the key here. So the best way to actually solve this question is by process of elimination, right? So let's take a look at a, let's see if this makes sense. So they say x minus five is a factor of p of x. So remember what a factor means.

That means if x here is five, five minus five is zero, that means my y is going to be zero, right? That means x is just one of the values that make y zero. So if I plug in five for x, so if P of five, or p of x is five, right? So if this whole thing here is P of five, then what is my value? Is it zero or not? Well, based on the information we're given, we can't really tell it could be and it could not be We're not really given any more information, we're only told about P of three, not P of five.

So when they say, which of the following has to be true or must be true? Well, we can't really say that a must be true. So let's cross that out. b, x minus two is a factor of p of x. So again, that means that if I plug in two for x, I should get zero. Well, is that true?

Well, again, it could be it could not be we're not giving any information about what P of two is. We're only given information about P of three. All right, so can't be be either. What about c? x plus two is a factor p of x. That means that if x is negative two, that means y would be zero or p of x would be zero.

Well, again, are we told anything about P of negative two? And No, we're not. We're only told about P of three. So therefore, we can All the first three out and your answer is D