Explanation for Question 25 From the Math (Calc) Section on the Official Sat Practice Test 4
So here for number 25, I'm going to start off by showing you how 2 to do the problem algebraically. And then we'll go in and I'll show you 3 the quicker, uh, Martin test taker, savvy way to do the problem. 4 And so if we're looking in at F of X here, first thing we 5 should be able to notice is that we can actually factor out a two 6 X, right? And when I do that, 7 that leaves me with X squared plus three X plus two. 8 And that's actually the same thing as G of X, 9 right? So what I really have here F of X is equal to 10 G of X, um, 11 times two X, right? The two X times G 12 of X. So now if I'm looking at my answer choices and I want 13 for there to be a factor of two X plus three, 14 let's take a look at answer choice B, right? 15 If I plug in F of X to be two X times G of 16 X, rather than, um, 17 you know, just G of X. And then I add plus three G of 18 X notice that G of X shows up in both my terms, 19 so I can actually factor it out here. So I factor out the, 20 um, the G of X and that leaves you with two X plus three. 21 And so since I have a two X plus three here, 22 it's like two X plus three is eight zero of my equation. 23 And if a polynomial is divisible by something by a term, 24 that means that it's a zero or it shows up when you factor it. 25 Um, for example, another good example would be if you had a function that 26 factored out, no, when you factored it, 27 you got this, then it would be divisible by two X plus three. 28 And so that makes our answer be algebr...