1974 AMC 12 Problem 4

Attempt Problem 4 of the 1974 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1974 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

What is the remainder when

x^{51}+51

is divided by

x+1?

0

1

49

50

51

For division by

x+1,

evaluate the polynomial at

-1

The exponent

51

is odd

By the polynomial remainder theorem, the remainder is

(-1)^{51}+51=-1+51=50.

Therefore, the correct answer is D.

Problem 4 in other years