TITLE: Question on Algebra
QUESTION [5 upvotes]: Let $P(x)$ be a fourth degree polynomial with coefficient of leading term be $1$ and  $P(1) = P(2) = P(3) = 0$, then find the value of $P(0) + P(4)$ .

REPLY [10 votes]: Hint:
as the coefficient term is 1
$$P(x)=(x-1)(x-2)(x-3)(x-a)$$, 
then $$P(0)+P(4)=6a+6(4-a)$$.