Question

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

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○A. The point (-c, 0) lies on the graph of f(x)

○B. The point (0, c) lies on the graph of f(x)

○C. x-c is a factor of f(x)

○D. x+c divides evenly into f(x)​

Answer 1

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.

Answer 2

C.

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.