<u>Complete Question:</u>
If (x + k) is a factor of f(x), which of the following must be true?
- f(k) = 0
- f(–k) = 0
- A root of f(x) is x = k.
- A y intercept of f(x) is x = –k.
<u>Correct Answer:</u>
If (x + k) is a factor of f(x), f(-k)=0 must be true
option B
<u>Step-by-step explanation:</u>
We have , (x + k) is a factor of f(x) . For this case we have a function of the form: . Thus,
x: independent variable
f (x): dependent variable
Since (x + k) is a factor of f (x) then it follows that:
For we have:
⇒
From here, we clear the value of x:
⇒
Then, replacing this value of x in the function, we have:
⇒
Therefore , Correct option B) f (-k) = 0.