If x⁵¹ + 51 is divided by x + 1, what is the remainder?

Correct answer: 50. By the remainder theorem, put x = −1: (−1)⁵¹ + 51 = −1 + 51 = 50.

Background: To divide by (x − a), put x = a.

• 49: 49 is not (−1)⁵¹ + 51.
• 51: 51 ignores the −1 from (−1)⁵¹.
• None of these: “None of these” is incorrect because 50 is correct.

Did you know? (−1) raised to an odd power is −1.

Memory trick: Put x = −1.