Question

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)
Responses

(x−0)
left parenthesis x minus 0 right parenthesis

(x−12)
left parenthesis x minus 12 right parenthesis

(x+12)
left parenthesis x plus 12 right parenthesis

(x−32)

Answer 1

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - c \), then the remainder of that division is equal to \( f(c) \). In this case, since it's given that \( f(12) = 0 \), it follows that when we divide \( f(x) \) by \( x - 12 \), the remainder is zero.

This implies that \( x - 12 \) is a factor of \( f(x) \).

Therefore, the correct response is:

**(x - 12)**