Given a polynomial f(x) and that f(12)=0, apply the Remainder Theorem and then determine which of the following is a factor of f(x).(1 point)
(x+12)
(x−0)
(x−3/2)
(x−12)
Given that f(12) = 0, we can apply the Remainder Theorem which states that if a polynomial f(x) is divided by (x-a), the remainder is equal to f(a). In this case, (x+12) is divided by (x-12) and the remainder should be 0 if (x-12) is a factor of f(x).
Therefore, we can conclude that (x-12) is a factor of f(x).
To apply the Remainder Theorem, we need to divide the polynomial f(x) by (x - a), where "a" is the value given in the problem. In this case, the value given is a = 12.
So, we will divide f(x) by (x - 12). If the remainder is zero, then (x - 12) is a factor of f(x).
Therefore, the correct choice is (x - 12).