Question

Given a polynomial f(x), if (x − 4) is a factor, what else must be true?

Answer 1

Answer:

$f(4)=0$

Step-by-step explanation:

The Remainder Theorem states that when you divide a polynomial $f(x)$  by a linear factor  $(x-a)$ , where $a$  is a constant, the remainder is $f(x)$  evaluated at $x=a$

Moreover, according to the Factor Theorem, an extension of the Remainder Theorem, if the remainder of the function $f(x)$ is 0 when evaluated at $x=a$ , then $(x-a)$  is said to be a factor of the polynomial $f(x)$

Given the 2 theorems above, it follows that if $(x-4)$  is a factor of $f(x)$ , then the remainder is equal to 0 when $f(x)$ is evaluated at $x=4$

Which means $f(4)=0$

Third answer choice is correct.

Answer 2

If x-a is the factor of f(x) then
f(a) = 0

Hence,
if x-4 is a factor of f(x) then f(4) = 0

option C