There's no information about F(x) to answer this question.
If there's a value of x for which F(x)=0, then, according to the Remainder Theorem, that value of x is a root (zero) for F(x). For example, if F(1)=0, then 1 is a zero of F(x), and (x-1) is a factor of F(x). The remainder after dividing F(x) would be zero.