Respuesta :

Complete Question:

If (x + k) is a factor of f(x), which of the following must be true?

  1. f(k) = 0
  2. f(–k) = 0
  3. A root of f(x) is x = k.
  4. A y intercept of f(x) is x = –k.

Correct Answer:

If (x + k) is a factor of f(x), f(-k)=0 must be true

option B

Step-by-step explanation:

We have , (x + k) is a factor of f(x) . For this case we have a function of the form: [tex]f(x)[/tex]. Thus,

x: independent variable

f (x): dependent variable

Since (x + k) is a factor of f (x) then it follows that:

For [tex]f(x)=0[/tex] we have:

⇒ [tex]x+k=0[/tex]

From here, we clear the value of x:

⇒ [tex]x=-k[/tex]

Then, replacing this value of x in the function, we have:

⇒ [tex]f(-k)=0[/tex]

Therefore , Correct option B) f (-k) = 0.

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