Question

Use synthetic division to rewrite the following fraction in the form q(x) + r(x)/d(x), where d(x) is the denominator of the original fraction, q(x) is the quotient, and r(x) is the remainder.

Answer 1

Answer

$\begin{gathered} \text{Let the given function be:} \\ \\ f(x)=\frac{3x^3-8ix^2+5x+(7-5i)}{x-2i} \end{gathered}$

Using the long division method, we have

Expressing the given expression in the form g(x) + r(x)/d(x), we have

$\begin{gathered} 3x^2-2ix+1+\frac{7-3i}{x-2i} \\ \text{Where} \\ g(x)=3x^2-2ix+1, \\ r(x)=7-3i\text{ and } \\ d(x)=x-2i \end{gathered}$