Question

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

f(0) = 4
f(0) = −4
f(4) = 0
f(−4) = 0
thank you in advance

Answer 1

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

Answer 2

`f(4)=0`

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.