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

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

B. x + c is a factor of f(x).

C. x-cdivides evenly into f(x).

D. The point (-c,0) does not lie on the graph of f(x).



Answer :

Answer:

C. x - c divides evenly into f(x).

Step-by-step explanation:

If f(c) = 0, it indicates that when the function f(x) is evaluated at x = c, the function is zero, implying that point (c, 0) lies on the graph of f(x).

The roots of a function are the x-values for which the function equals zero. Therefore, given that f(x) = 0, then x = c is a root of function f(x). The factor theorem states that if a polynomial function f(x) has a root at x = c, then (x - c) is a factor of f(x). So, given that f(c) = 0, then (x - c) is a factor of f(x).

If (x - c) is a factor of f(x), and f(x) = 0, then (x - c) divides evenly into f(x).

Without further information about the function f(x), we cannot definitively state whether the point (-c, 0) lies on the graph of f(x).

Therefore, the only true statement from the given answer options is option C:

[tex]\Large\boxed{\textsf{$x - c$ divides evenly into $f(x)$.}}[/tex]