HMMT 十一月 2012 · GEN 赛 · 第 2 题
HMMT November 2012 — GEN Round — Problem 2
题目详情
- [ 3 ] Let Q ( x ) = x + 2 x + 3, and suppose that P ( x ) is a polynomial such that 6 5 4 3 2 P ( Q ( x )) = x + 6 x + 18 x + 32 x + 35 x + 22 x + 8 . Compute P (2).
解析
- [ 3 ] Let Q ( x ) = x + 2 x + 3, and suppose that P ( x ) is a polynomial such that 6 5 4 3 2 P ( Q ( x )) = x + 6 x + 18 x + 32 x + 35 x + 22 x + 8 . Compute P (2). Answer: 2 Note that Q ( − 1) = 2. Therefore, P (2) = P ( Q ( − 1)) = 1 − 6+18 − 32+35 − 22+8 = 2.