Explanation for Question 7 From the Math (No Calc) Section on the 2019 April Sat
For number seven, we were looking for an expression equivalent to the one that 2 we are given. And just by looking at these answer choices, 3 you can tell that what you're looking to do here is to factor. 4 So we can go ahead and factor this original expression, 5 like a normal polynomial. So we're looking for two numbers that multiply to 6 16 and add up to negative rate. 7 Those two numbers would be negative four and negative four. 8 So now that we have that, we can rewrite it as X to the 9 fourth, minus four X squared, 10 minus four X squared, plus 16. 11 From this first half, you can factor out an X squared leaves you with 12 X squared minus four. And then from the second half, 13 you can factor out a negative four that also leaves you with X 14 squared minus four. So our factored form is X squared, 15 minus four times X squared, 16 minus four. 17 If you had felt confident enough after getting these two numbers to jump to 18 this step, that is perfectly okay too. But sometimes it's helpful to write it 19 all out just in case to be on the safe side. 20 So now, if we look at our answer choices, 21 that is not any of the answers and that is because X squared minus 22 four can be factored even further. 23 If you recall the general format, 24 a squared minus B squared equals a plus B times 25 a minus B, that is the difference of squares, 26 which is what X squared minus four is. So using that, 27 you know, that X squared minus four can factor into X plus two 28 times X minus tw...