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

`\begin{gathered} \text{Let the given function be:} \\ \\ f(x)=(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+(7-3i)/(x-2i) \\ \text{Where} \\ g(x)=3x^2-2ix+1, \\ r(x)=7-3i\text{ and } \\ d(x)=x-2i \end{gathered}`