you are told that f(x) is a polynomial?

Question

and you are told that when we divide x + 1 into f(x) then the remainder is 0. Based on this information which of these statements is necessarily true?
a= f(1)=0
b= f(0)=1
c= f(-1)=0
d= f (0)=-1

Answer 1

If f(x) divisible by x+1 with no remainder, then
f(x) = (x+1)*Q(x)
So f(-1) = (-1+1)Q(x) = 0*Q(x)=0
The answer is c: f(-1) =0

Answer 2

The remainder theorem says: If p is a polynomial over
the rationals and x-a is a factor of p then a is a zero of p.
So the answer is c: f(-1) = 0.

Answer 3

c) This is remainder theorem.

Answer 4

C