How do you divide (20x^4+(5-12i)x^3-(25+3i)x^2+15ix)/(5x-3i) ?
2 Answers
(20x^4+(5-12i)x^3-(25+3i)x^2+15ix)/(5x-3i) = 4x^3+x^2-5x
Explanation:
The first term in the quotient is
Then
Subtract this from the dividend:
(20x^4+(5-12i)x^3-(25+3i)x^2+15ix)-(20x^4-12ix^3)
=5x^3-(25+3i)x^2+15ix
The next term in the quotient is
Then
Subtract this from the remainder:
(5x^3-(25+3i)x^2+15ix)-(5x^3-3ix^2)=-25x^2+15ix
The next term in the quotient is
Then
...equalling the remainder.
So:
(20x^4+(5-12i)x^3-(25+3i)x^2+15ix)/(5x-3i)
= 4x^3+x^2-5x