PolynomialAndEquation Intermediate

Problem - 3265
Let $P(x)$ be a monic polynomial of degree 3. (Monic here means that the coefficient of $x^3$ is 1.) Suppose that the remainder when $P(x)$ is divided by $x^2 - 5x+6$ equals 2 times the remainder when $P(x)$ is divided by $x^2 - 5x + 4$. If $P(0) = 100$, what is $P(5)$?

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