Question

If f(k) = 0, which of the following statements must be true?

x- k is a factor of f(x).
The point (k,0) lies on the graph of f(x).
k is a 0 for f(x).
All are true

I think A is right...but not sure if any of the others are?

Answer 1

All are correct

Answer 2

However, the first statement is only true for algebraic functions. Something like f(x) = sin(x) doesn't have x as a factor (well, it does if you write sin(x) out in a taylor series, but that is second semester university maths, I assume you are not in uni).

Answer 3

for f(x)= sin(x) , f(0) = 0 , but x is not an explicit factor of the function.