Explanation for Question 17 From the Math (No Calc) Section on the 2019 April Sat
So for number 17, we are given the equation above where a is a 2 constant, and we are looking for the value of a, 3 that makes the equation true for all values of X. 4 So I'm going to start off by trying to make the left side of 5 the equation, look like the right side. And first I'll distribute this 6 entire left side. So that gives me five X plus 7 five plus three X squared, 8 minus three, a equals the three X 9 squared plus five X plus four. 10 So now I can combine like terms three X squared has nothing to combine 11 with. So I'll write that first. 12 Then we have only one term with an X, 13 so that can't combine with anything either. 14 Then we have five, a minus three, 15 a, which will leave me with two eight. 16 And all of that is still equal to three X squared plus five X 17 plus four. 18 So in order for the equation to be true, 19 they have to be exactly identical. 20 So the three X squared matches up the five X matches up. 21 So that means this two way is going to match up with this four. 22 So two a is equal to four. 23 You can also go ahead and start subtracting everything. 24 So I can subtract the three X squared from both sides and 25 get rid of it leaves me with five X plus two equals 26 five X plus four. And then you can subtract the five X that 27 gets rid of it on both sides, which leaves you with two eight equals 28 four, which is when I got the four. 29 So now to solve for a, you can just divide both sides by two, 30 which gives you a, 31 is equal to two.