When f(x)=x4−5x3+8x

Question

is divided by x−3
, its remainder is -30. Which of the following is correct according to the Remainder Theorem?(1 point)
Responses

f(−3)=30
f of negative 3 is equal to 30

f(−3)=−30
f of negative 3 is equal to negative 30

f(3)=−30
f of 3 is equal to negative 30

f(3)=30

Answer 1

According to the Remainder Theorem, when a polynomial \( f(x) \) is divided by \( x - c \), the remainder is equal to \( f(c) \).

In your case, you have \( f(x) = x^4 - 5x^3 + 8x \) and when it is divided by \( x - 3 \), the remainder is given as -30. According to the Remainder Theorem, this means:

\[ f(3) = -30 \]

So the correct response is:

f(3) = -30
f of 3 is equal to negative 30