Problem #25 in the calculator-allowed section of Practice Test #4, please.
This is a fun question! First, note that the polynomials provided have a little something in common:
Do you see it? How about now:
Takeaway lesson from that: when a question at first looks like it might take a very long time to do (in this case, when it looks at first like you’re going to have to do long division possibly four times) slow down for a minute and think about whether there’s a shortcut built into the problem.
You’re looking for a way to combine and so that they’re divisible by . Once you see that you can pull a (as in, the same that’s part of ) out of and get , you know to use that as your base of operations. Let’s just see what happens if we multiply by :
Ready for the last step? All we need to do is substitute because we know :
That matches choice B, and we know that it’s divisible by because we made it by multiplying by !