Could you please explain how to do question #7 from math section #3 from the Official SAT Test #3? Thanks so much! Your book rocks my socks off.

You bet, and thanks for the compliment! 🙂

The thing to recognize here is that when (x – a) is a factor of a polynomial, then that polynomial has a zero at x = a, and when a polynomial has a zero at x = a, then (x – a) is a factor of that polynomial. (In other words, it works both ways.)

Since the table in this question tells you that f(4) = 0, you know that (x – 4) is a factor of f(x).