[Video] Q7: The function f is defined by a polynomial. some values of x and f (x) are shown in the table above. which of the following must be a factor of f (x)?

Explanation for Question 7 From the Math (No Calc) Section on the Official Sat Practice Test 3

Not for question number seven, we're given a table with X and F of 2 X values. And just as a reminder, 3 whenever you see F of X, it's just a fancy way of saying the 4 Y coordinate. And so it tells us that it's a polynomial. 5 Um, that just means that it might look something like X squared plus two 6 X plus one, right? So it's got multiple, 7 multiple terms with different exponents and some of the values of X and F 8 of X are shown above. And then it asks us what must be a 9 factor of F of X, 10 right? And so we can think about when you have a polynomial and you're 11 asked to factor it. Um, 12 for example, I believe this one would factor this way, 13 X plus one times X plus one. Um, 14 when you factor it out, you get these little, 15 or I guess what I call a double bubble, right? 16 Where you get to a set of two parentheses. 17 And then from there you always take a parentheses and set it equal to 18 zero, right? And then that will give you the zero of the function. 19 X is equal to negative one, which essentially means that when X is negative, 20 one, Y is equal to zero. 21 So what we're going to do here is we want to find a point 22 where our Y value, our F of X is equal to zero. 23 And we see that that happens when X is equal to four. 24 So I'm going to take a second. I'm going to say X is equal 25 to four, and now I'm going to kind of work backwards. 26 Right? I actually started at this point, 27 but I want to get up here to my factors. 28 So I'll do that by moving the four to the other side, 29 I see that I get X minus four is equal to zero, 30 which means that whatever the polynomial is here, 31 if you were to factor it, one of your bubbles would have an X 32 minus four. And so our best answer here is going to be C.