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.
