Answer:
b)
Explanation:
If x - 2 is a factor polynomial f(x), then the polynomial can be expressed as f(x) = (x - 2) g(x), where g(x) is another polynomial.
Using this information, we can check each statement to see which one does NOT have to be true:
A) f(2) = 0:
If x - 2 is a factor of f(x), then plugging in x = 2 gives f(2) = (2 - 2) g(2) = 0. This statement has to be true.
B) f(-2) = 0:
If x - 2 is a factor of f(x), then plugging in x = -2 gives f(-2) = (-2 - 2) g(-2) = -4 g(-2). This statement does NOT have to be true. For example, if g(-2) = 1/(-4), then f(-2) would not equal 0.
C) 2 is a root of f(x):
If x - 2 is a factor of f(x), then 2 is a root of f(x), meaning f(2) = 0. This statement has to be true.
D) 2 is a zero of f(x):
The term "zero" can be interpreted in different ways, but if it means the same as a root or a solution, then this statement is the same as statement C and has to be true.
Therefore, the statement that does NOT have to be true is B) f(-2) = 0.