Explanation for Question 4 From the Math (No Calc) Section on the Official Sat Practice Test 6
Question four gives us this expression. 2 And then it says in the equation above P and T are constants, 3 which of the following could be the value of P all right. 4 So we've got four X squared minus nine is equal to 5 P X plus T times P X minus T. 6 So hopefully this looks familiar to you and you can tell that this right 7 here is going to be the factored form of this left side of the 8 expression. So it's trying to think of how we could factor this 9 one out first. I like to always check and see if there's in a 10 multiplying factor that you can pull out in front. So for example, 11 if you could say four times X squared minus something, 12 but we can see if there's not, um, four and nine, 13 don't share any common, common, 14 um, multipliers. So let's write out, 15 we want it to look like something X plus something, 16 times something X plus something. 17 And we know that to get four X squared, 18 it's either going to be a four here and a one here or a 19 two here, two here, but we know that it's going to be a two 20 here and a two here, because we know that P is equal to P. 21 We know that that variable has to be the same. 22 So from that, we can pick a, 23 is our answer and move on. You might be confused by the 24 fact that they also have this plus T right here, 25 and you could solve that through. Um, and I can go through how to 26 do that. But for the sake of this answer choice, 27 you really only need to solve for a to find the other part. 28 What I would recommend doing is multiplying out to see 29 what or figuring out which multiplies could get you to nine. 30 So in this case, that's going to be plus three, 31 and then this is actually going to be minus three. 32 And that's how you would factor out this expression. 33 And then if you foil through and check it, 34 you'll get four X squared minus 35 six X plus six X minus nine. 36 And sure enough, that is four X squared minus nine.