Question

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

Answer 1

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 2

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.