Use the remainder theorem and synthetic division to find f(k).
-$k = - 3 + 2 i ; f ( x ) = x ^ { 2 } - 5 x - 5$
A) -7
B) 15-22i
C) 15-16i
D) 20-16i

Question

Use the remainder theorem and synthetic division to find f(k).
-$k = - 3 + 2 i ; f ( x ) = x ^ { 2 } - 5 x - 5$
A)  -7 
B)  15-22i
C)  15-16i 
D)  20-16i

Quizplus · Accepted Answer

Given $k = -3 + 2i$, to find $f(k)$ using the remainder theorem, we substitute $k$ into $f(x)$: $f(k) = (-3 + 2i)^2 - 5(-3 + 2i) - 5$. Simplifying, $f(k) = 9 - 12i + 4i^2 + 15 - 10i - 5$. Since $i^2 = -1$, $f(k) = 9 - 22i - 4 + 15 - 5 = 15 - 22i$.

Use the Remainder Theorem and Synthetic Division to Find F(k) k=−3+2i;f(x)=x2−5x−5k = - 3 + 2 i ; f ( x ) = x ^ { 2 } - 5 x - 5k=−3+2i;f(x)=x2−5x−5

Use the Remainder Theorem and Synthetic Division to Find F(k) $k = - 3 + 2 i ; f ( x ) = x ^ { 2 } - 5 x - 5$