Question

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

A. The point (c,0) lies on the graph of f(x)
B. x - c is a factor of f(x).
C. c is a 0 for f(x).
D. All three statements are true.

Answer 1

Answer: D) All three statements are true.
Thank you.

Answer 2

For this case suppose we have a function of the form:

y = f (x)

Where,

x: independent variable

y: dependent variable

We have then that the value of the function for x = c is:

f (c) = 0

Therefore, we have that:

The point (c, 0) belongs to f (x)

x-c is a common factor of f (x) because the function evaluated at x = c is equal to zero.

x = c is a root of f (x) so c is a zero of the function f (x)

Answer:

D. All three statements are true.