Answer:
C.
Step-by-step explanation:
If f(c)=0 then (c,0) is on the graph.
In general, if f(a)=b then (a,b) is on the graph.
By factor theorem if f(c)=0 then x-c is a factor.
If x-c is a factor then x-c will divide f(x) evenly. We know this because the remainder will be 0 because we know x-c is a factor of f.
The only choice that I have said in this whole thing that is true is C.
Answer: The correct option is
(C) x-c is a factor of f(x).
Step-by-step explanation: Given that for a function f(x), f(c) = 0.
We are to select the true statement from the given options.
We have the factor theorem as follows :
Factor theorem : If p(a) = 0 for a polynomial function p(x), then (x-a) is a factor of p(x).
According to the given information, we have
f(c) = 0.
Therefore, (x-c) is a factor of f(x).
Thus, (C) is the correct option.
