What is the remainder when a³ − 8a − 8 is divided by a + 1?

Correct answer: b −1

f(−1) = (−1)³ − 8(−1) − 8 = −1 + 8 − 8 = −1.

Why the other options are wrong

• a −15: −15 is f(1) = 1 − 8 − 8, which would be the remainder for divisor a − 1. For a + 1 put a = −1.
• c 0: 0 would mean a + 1 is a factor; but f(−1) = −1, not zero.
• d 1: 1 is the sign-flipped answer; −1 + 8 − 8 = −1, not +1.