College Algrebra
posted by Anonymous .
How would you use synthetic division to find the quotient and remainder for this problem:
(X^3+3ix^24ix2)/(x+i)

The same way you do it normally. Just keep track of the i's and remember that i^2 = 1
So, the rows of coeffiicients are (munged by font spacing)
1 3i 4i 2 (i
0 i 4 4i+4
_____________
1 4i 44i 24i
So that means that
(x^3 + 3ix^2  4ix  2)/(xi)
= x^2 + 4ix  (4+4i) remainder 24i
If you multiply it out, it works.