1977 AMC 12 Problem 28
Attempt Problem 28 of the 1977 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 1977 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
Let What is the remainder when the polynomial is divided by the polynomial
Answer: A
Small hint:
Use
Big hint:
Evaluate the remainder at the five roots of and use its degree bound
Solution:
Let be the remainder, so The five roots of satisfy and Hence and Therefore a polynomial of degree at most has five distinct roots. It must be identically zero, so
Therefore, the correct answer is A.
Problem 28 in other years
- 1950 AMC 12
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