Use the remainder theorem and synthetic division to find f(k).
-$$\mathrm { k } = 2 ; \mathrm { f } ( \mathrm { x } ) = - \mathrm { x } ^ { 3 } - 2 \mathrm { x } ^ { 2 } + 4$$
A) $- 12$
B) 3
C) 9
D) 12

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 $f(x) = -x^3 - 2x^2 + 4$ and $k = 2$, we perform synthetic division with 2:$$\begin{array}{r|rrr}2 & -1 & -2 & 0 & 4 \\hline& & -2 & 0 & 0 \& -1 & -4 & 0 & 4 \\end{array}$$The remainder, which is $f(2)$, is $-12$.

Use the Remainder Theorem and Synthetic Division to Find F(k) k=2;f(x)=−x3−2x2+4\mathrm { k } = 2 ; \mathrm { f } ( \mathrm { x } ) = - \mathrm { x } ^ { 3 } - 2 \mathrm { x } ^ { 2 } + 4k=2;f(x)=−x3−2x2+4

Use the Remainder Theorem and Synthetic Division to Find F(k) $\mathrm { k } = 2 ; \mathrm { f } ( \mathrm { x } ) = - \mathrm { x } ^ { 3 } - 2 \mathrm { x } ^ { 2 } + 4$