1950 AMC 12 Problem 20

Attempt Problem 20 of the 1950 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 1950 AMC 12 solutions, or check the answer key.

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

20.

When

x^{13}+1

is divided by

x-1,

the remainder is:

1

-1

0

2

None of these answers

Use the Remainder Theorem

For division by

x-1,

evaluate the polynomial at

x=1

By the Remainder Theorem, the remainder upon division by

x-1

is the value of the polynomial at

x=1.

This value is

1^{13}+1=2.

Thus, the correct answer is D.

Problem 20 in other years