MathDB

4

Part of 2012 CHMMC Spring

Problems(2)

2012 Spring Team #4

Source:

3/20/2022
Let P(x)P(x) be a monic polynomial of degree 33. Suppose that P(x)P(x) has remainder R(x)R(x) when it is divided by (x−1)(x−4)(x - 1)(x - 4) and 2R(x)2R(x) when it is divided by (x−2)(x−3)(x - 2)(x - 3). Given that P(0)=5P(0) = 5, find P(5)P(5).
algebra
2012 Spring CHMMC Tiebreaker 4 - numbers 1-6 in fractions, min result

Source:

3/1/2024
The expression below has six empty boxes. Each box is to be fi lled in with a number from 11 to 66, where all six numbers are used exactly once, and then the expression is evaluated. What is the maximum possible final result that can be achieved?
□□+□□□□\dfrac{\frac{\square}{\square}+\frac{\square}{\square}}{\frac{\square}{\square}}
algebraCHMMC