# !Fancy cubic

Author: anonymous
Problem has been solved: 64 times

Русский язык | English Language

The cubic polynomial $P (x)$ is given. For a certain number $a$, we define $P_1(x) = x^2 + (a-29) x-a$ and $P_2(x) = 2x^2 + (2a-43)x + a$. It turned out that $P(x)$ is divisible by $P_1(x)$ and $P_2(x)$. Find the largest possible value of $a$.