Explanation for Question 18 From the Math (No Calc) Section on the Official Sat Practice Test 4
Not for number 18, we're asked what real value of X is the equation 2 above true. And when they ask you that they really mean, 3 you know, solve for X. And so as we rewrite it here, 4 you know, we see we've got some cubes. We see we've got some squared 5 terms. So that means if we're going to solve for X, 6 we have to factor, but you need to know how to factor with four 7 terms in order to do this problem. And so when you want to factor 8 with four terms, you start by separating it into two sets of parentheses. 9 And then you look at both of your parentheses and you pull out the 10 greatest common factor. And our left parentheses are G C F is 11 X squared. When I pull that out, 12 that leaves me with X minus five. Now for our right-hand parentheses, 13 our GCF is two. 14 When I factor out a two I'm left with X minus five. 15 So now I need to rewrite this with two parentheses instead of, 16 you know, three in some numbers in my first friend, 17 the C I just put whatever was already in parentheses. 18 And then the leftover parentheses, we drop whatever numbers we had on the outside, 19 which in this case was X squared plus two. So to solve for X, 20 we need to take our two expressions and set them equal to zero. 21 And so in our expression on the right, if I try to solve it, 22 I get X squared is equal to negative two. Then I need the square 23 root, right. But I can't square root a negative. 24 My solution needs to be real. 25 So this parentheses gives me no, no answer, 26 but if I solve for X with the X minus five, 27 I get the X is equal to five, which is a real normal number. 28 This is our answer. Then to number 18 is five.