Expert: Paul Klarreich - 8/22/2009

Question
Divide 3x^3+2x^2+4x-1 by x^2+1. What is the quotient?

Answer
Questioner: Zarak
Country: United States
Category: Advanced Math
Private: No
Subject: Polynomial Division
Question: Divide 3x^3+2x^2+4x-1 by x^2+1. What is the quotient?
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FIRST DIVISION:

x^2 + 1  ))  3x^3 + 2x^2 + 4x - 1  (( 3x
            3x^3        + 3x
           -------------------  << subtract
                   2x^2 +  x - 1


SECOND DIVISION:
x^2 + 1  ))  3x^3 + 2x^2 + 4x - 1  (( 3x + 2  << quotient
            3x^3        + 3x
           -------------------  << subtract
                   2x^2 +  x - 1
                   2x^2      + 2
                  --------------- << subtract
                           x - 3  << remainder has lower degree than divisor.