Answer:
f(2)=0. The third option is correct.
Step-by-step explanation:
Suppose we have a polynomial called f(x) and we know (x-2) is a factor of f. This means that we can express f(x) as:
f(x)=(x-2)\cdot g(x)
Being g(x) another unknown function.
Option 1: f(0)=(0-2)\cdot g(0)=-2\cdot g(0). Since we don't know the value of g(0), we cannot assure f(0)=-2. Incorrect
Option 2: f(-2)=(-2-2)\cdot g(-2)=-4\cdot g(-2). Since we don't know the value of g(-2), we cannot assure f(-2)=0. Incorrect
Option 3: f(2)=(2-2)\cdot g(2)=0\cdot g(0)=0. Regardless of the value of g(0), f(0) must be 0. Correct
Option 4: f(0)=(0-2)\cdot g(0)=-2\cdot g(0). Since we don't know the value of g(0), we cannot assure f(0)=2. Incorrect
