Use the remainder theorem and synthetic division to find f(k).
-$$k = 3 : f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 2$$
A) 4
B) 7
C) 48
D) -7

Question

Quizplus · Accepted Answer

The remainder theorem states that if a polynomial $f(x)$ is divided by $x - k$, the remainder is $f(k)$. For $k = 3$, we perform synthetic division or directly substitute $x = 3$ into the polynomial. Substituting $x = 3$ into $f(x) = -x^3 + 2x^2 + 2$, we get $f(3) = -(3)^3 + 2(3)^2 + 2 = -27 + 18 + 2 = -7$.

Use the Remainder Theorem and Synthetic Division to Find F(k) k=3:f(x)=−x3+2x2+2k = 3 : f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 2k=3:f(x)=−x3+2x2+2

Use the Remainder Theorem and Synthetic Division to Find F(k) $k = 3 : f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 2$