Use the remainder theorem and synthetic division to find f(k).
-$\mathrm { k } = 2 + \mathrm { i } ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } + 10$
A) $12 + 11 \mathrm { i }$
B) $2 + 11 \mathrm { i }$
C) $12 + 12 \mathrm { i }$
D) $2 + 12 \mathrm { i }$

Question

Quizplus · Accepted Answer

Given $f(x) = x^3 + 10$ and $k = 2 + i$, to find $f(k)$, we substitute $x = 2 + i$ into $f(x)$: $f(2 + i) = (2 + i)^3 + 10$. Expanding $(2 + i)^3$ gives $8 + 12i + 6i^2 + i^3$. Since $i^2 = -1$ and $i^3 = -i$, this simplifies to $8 + 12i - 6 - i + 10$, which equals $12 + 11i$.

Use the Remainder Theorem and Synthetic Division to Find F(k) k=2+i;f(x)=x3+10\mathrm { k } = 2 + \mathrm { i } ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } + 10k=2+i;f(x)=x3+10

Use the Remainder Theorem and Synthetic Division to Find F(k) $\mathrm { k } = 2 + \mathrm { i } ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } + 10$