If you have questions about anything I have posted, I am easy to find and happy to discuss these posts and more. But I have to ask you to find me through my work or twitter…I am not hard to google. I have disabled the email feature here due to a ridiculous quantity of spam!

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Hi. I have your New SAT Game Plan book. Have tried to follow your suggestions for dealing with functions. There was a question on a Princeton Review SAT Practice test my nephew took a few weeks ago. I have been tutoring him with your book. Maybe you can tell us how to approach this. We are lost.

f(x) = ax^3 + bx^2 + cx + d.

a,b,c and d are constants. If f(-5)=3, which of the following must be true about f(x)?

A) x – 3 is a factor of f(x)

B) The remainder when f(x) is divided by x + 5 is 3.

C) x + 2 is a factor of f(x)

D) x + 5 is a factor of f(x)

I have your older version book, so if it’s covered in the new book, let me know. I didn’t think the math changed that much in the new version of the test.

Thanks!

Hello,

The math has in fact changed a lot! This question is asking about something called the remainder theorem. I’ll try to be brief…

Say you have a polynomial, f(x). If some number, c, is a root of that polynomial, that means two things:

1. f(c) = 0

2. When you divide f(x) by x-c, it divides evenly and you get no remainder.

On the other hand, if c is NOT a root, then when you divide f(x) by x-c you get a remainder. And the remainder theorem says that the remainder will also be what you get when you evaluate f(c).

So in this problem, since f(-5) is 3 (and not zero), we know that (x+5) does not divide f(x) evenly. It has a remainder of 3.

And yes, this is covered in the new book 🙂