Answer:
[tex]f(4)=0[/tex]
Step-by-step explanation:
The Remainder Theorem states that when you divide a polynomial [tex]f(x)[/tex] by a linear factor [tex](x-a)[/tex] , where [tex]a[/tex] is a constant, the remainder is [tex]f(x)[/tex] evaluated at [tex]x=a[/tex]
Moreover, according to the Factor Theorem, an extension of the Remainder Theorem, if the remainder of the function [tex]f(x)[/tex] is 0 when evaluated at [tex]x=a[/tex] , then [tex](x-a)[/tex] is said to be a factor of the polynomial [tex]f(x)[/tex]
Given the 2 theorems above, it follows that if [tex](x-4)[/tex] is a factor of [tex]f(x)[/tex] , then the remainder is equal to 0 when [tex]f(x)[/tex] is evaluated at [tex]x=4[/tex]
Which means [tex]f(4)=0[/tex]
Third answer choice is correct.
