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+12)
left parenthesis x plus 12 right parenthesis
(x−12)
left parenthesis x minus 12 right parenthesis
(x−32)
left parenthesis x minus Start Fraction 3 over 2 End Fraction right parenthesis
(x−0)
1 answer
The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - c \), the remainder of that division is \( f(c) \). If \( f(c) = 0 \), it means that \( x - c \) is a factor of the polynomial \( f(x) \).
Given that \( f(12) = 0 \), we can conclude that \( x - 12 \) is a factor of \( f(x) \).
Thus, the correct answer is:
(x−12).
