Explanation for Question 16 From the Math (No Calc) Section on the Official Sat Practice Test 8
So question number 16 wants to know what AI is, 2 where AI is a solution to the equation in a is greater than zero. 3 So if aims a solution to the equation and the equation is a quadratic, 4 we find our solution by factoring, 5 right? And when we think about factoring, 6 we want to think about what numbers do we want to multiply to get 7 our numbers and what numbers do we want to add together? 8 And so the basic format is going to be two parentheses, 9 both of which start with an X. So now we're looking for these second 10 numbers here that we're going to put in. Now we want them to multiply, 11 to give us a negative 12, and we want them to add, 12 to give us positive one. And so we can think about working with four 13 and three. Now, if I make the four positive and the three negative, 14 and I multiply those together, I'll get negative 12. 15 And if I add those together, four minus three or four plus negative three, 16 right? We'll get positive one. So the answers that I want are 17 these right? And the next thing that I need to do is solve. 18 So if I do X plus four is equal to zero and I subtract 19 four from both sides by X is equal to four negative four. 20 And if I do X minus three equals zero, and I add three to 21 both sides, I get the X is equal to three. 22 So now the question is, oh, what answer choice do I write down? 23 I have a negative four and I have a three. But if we look 24 here at a, we can see the, a has to be greater than zero. 25 So my X has to be three. And so our answer is going to 26 be three.