[Video] Q8: F(x) = x^3 - 9x g(x) = x^2 - 2x -3 which of the following expressions is equivalent to f(x)/g(x), for x > 3 ?

Explanation for Question 8 From the Math (No Calc) Section on the Official Sat Practice Test 8

So question number eight gives us two functions F of X and G of 2 X. And then it asks us for F of X divided by G of 3 X. Right? And one thing that might be tripping you off on this question, 4 and that is that it says for X is greater than three, 5 but for now, let's just ignore that and then I'll show you why they 6 put that after we've kind of gotten started on the work, 7 right? And so if we're doing F of X over G of X, 8 a very simple and easy first step is just to write the function that's 9 F of X and then put it over the function 10 that is G of X, which is X squared, minus two X minus three. 11 And so now we can think to ourselves, okay, well, 12 that's not the answer. I obviously have to do some simplification here. 13 So what I can do to simplify is try to factor out anything that 14 I can here. Not for the numerator. 15 I can pull out an X, right? Because both terms have an X in 16 them. So if I factor out an X that leaves me with X squared 17 minus nine, and then on the bottom, 18 the bottom, I can simply factor all the way out, 19 right? I get X X because of the X squared. 20 And then I want to pick a number that multiplies to make negative three 21 and ask to make negative two. Now, 22 if I do negative three and positive one, 23 I add to get negative two, right? Cause one minus three is negative two. 24 And then negative three times one is negative three. 25 So these are the numbers that I want. Negative three and positive one. 26 And so here we can see that it ...