HMMT 二月 2001 · 团队赛 · 第 4 题
HMMT February 2001 — Team Round — Problem 4
题目详情
英文原题
- P is a polynomial. When P is divided by x − 1, the remainder is − 4. When P isdivided by x − 2, the remainder is − 1. When P is divided by x − 3, the remainder is 4.
3 2
Determine the remainder when P is divided by x − 6 x + 11 x − 6.
π π 4 1 2
解析
英文解析
- P is a polynomial. When P is divided by x − 1, the remainder is − 4. When P isdivided by x − 2, the remainder is − 1. When P is divided by x − 3, the remainder is 4.
3 2
Determine the remainder when P is divided by x − 6 x + 11 x − 6.
Solution: The remainder polynomial is simply the order two polynomial that goesthrough the points (1 , − 4), (2 , − 1), and (3 , 4): x − 5 .2
π π 4 2 1