(Confusing~~)When you have P(x) = X^^3 + X + 42,
you are trying to test if P(x) is factorized by
X + 42.
Then this problem is equivalent to testing
if Q(X) = X^^3 is factorized (divided) by X+42.
Then plugging in (-42) into X of Q(X) gives
(-42)^^3 is not zero.
But if X = 7 ,
X^^3 is divide by X+42=49.
What is the real trouble here?