SOLUTION: Please help me solve this polynomial division problem: x^4-3x^3+x^2-x-15 divided by x^2-x+2

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Question 198859This question is from textbook McDougal Littell Algebra 1
: Please help me solve this polynomial division problem:
x^4-3x^3+x^2-x-15 divided by x^2-x+2 This question is from textbook McDougal Littell Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To divide %28x%5E4-3x%5E3%2Bx%5E2-x-15%29%2F%28x%5E2-x%2B2%29, we need to use polynomial long division


Polynomial Long Division: 

                       x^2 -2x - 3
        -----------------------------
x^2-x+2 ) x^4 - 3x^3 + x^2 - x - 15
          x^4 -  x^3 +2x^2
         -----------------
               -2x^3 - x^2 - x
               -2x^3 +2x^2 -4x 
               ---------------
                     -3x^2 +3x - 15
                     -3x^2 +3x -  6
                     --------------
                                 -9


So %28x%5E4-3x%5E3%2Bx%5E2-x-15%29%2F%28x%5E2-x%2B2%29=x%5E2-2x-3-9%2F%28x%5E2-x%2B2%29


which also looks like


%28x%5E4-3x%5E3%2Bx%5E2-x-15%29%2F%28x%5E2-x%2B2%29=x%5E2-2x-3 remainder -9