By the Remainder Theorem, what can be said about the polynomial function z(x) if the remainder is −4 when z(x) is divided by x−2 ?

Answer 1

One thing for sure is that 2 is not a zero of the polynomial. In other words, (x-2) is not a factor of the polynomial since there is a remainder. For 2 to be a zero of the polynomial, the remainder would be zero.