[Video] Q29: For a polynomial p(x), the value of p(3) is -2 which of the following must be true about p(x)?

Explanation for Question 29 From the Math (Calc) Section on the Official Sat Practice Test 1

So right now we're looking at question number 29 and we see this asking 2 us about factors, right? It tells us that P of three is equal to 3 negative two, and it wants to know which of the following must be true 4 about P of X. So now, 5 if we look at an example that I've come up with here, 6 this isn't necessarily what P is, but just an example, 7 we can see that this could be a factor polynomial, 8 right? It could be X minus eight over or times X plus three. 9 And if these were a factor, you might remember synthetic division. 10 Right? And so if I were to take a, 11 and then let me do the math here real quick, 12 and then do synthetic division for this, I would get a remainder of zero. 13 Right? So if something is a factor, then I get a remainder of zero. 14 And also if something is a factor, then my answer would be zero as 15 well. Right? Like say that I wanted to find P of eight. 16 If I go into find P of eight and I plug eight in here, 17 eight minus eight is zero. And I get an answer of zero, 18 right? So since we'd got a negative two for P of three, 19 that means that negative three, right? 20 So X minus three is not a factor, 21 but they don't actually show us that. Right. 22 And in all actuality, we can't say anything about these other factors because we 23 don't have those numbers to work with. They didn't tell us anything about five. 24 They didn't tell us anything about two and they didn't tell us anything about 25 negative two. Right? All we know is about negativ...