Solve the problem.
-Use synthetic division and the remainder theorem to determine if $$[ x - ( 3 - 2 i ) ]$$ is a factor of $$f ( x ) = x ^ { 2 } - 6 x + 13$$
A) No
B) Yes

Question

Quizplus · Accepted Answer

To determine if $[x - (3 - 2i)]$ is a factor of $f(x) = x^2 - 6x + 13$, we use the remainder theorem. According to the theorem, if $f(c) = 0$ for some value $c$, then $(x - c)$ is a factor of $f(x)$. Here, $c = 3 - 2i$. We substitute $c$ into $f(x)$:$$f(3 - 2i) = (3 - 2i)^2 - 6(3 - 2i) + 13$$$$= (9 - 12i + 4i^2) - (18 - 12i) + 13$$$$= 9 - 12i - 4 - 18 + 12i + 13$$$$= 0$$Since $f(3 - 2i) = 0$, $[x - (3 - 2i)]$ is indeed a factor of $f(x)$.

Solve the Problem [x−(3−2i)][ x - ( 3 - 2 i ) ][x−(3−2i)]

Solve the Problem $[ x - ( 3 - 2 i ) ]$