SOLUTION: Can you help me simplify (not "solve") x - 3 divided by x^3 + x^2 - 10x - 6

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Question 392657: Can you help me simplify (not "solve")
x - 3 divided by x^3 + x^2 - 10x - 6
Found 2 solutions by rfer, Edwin McCravy:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
(x^3+x^2-10x-6)/(x-3)
x^2-6x+2 with R of 0

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Can you help me simplify (not "solve") %28x-3%29%2F%28x%5E3%2Bx%5E2-10x-6%29 

The other tutor divided the wrong way.

x - 3 divided by x^3 + x^2 - 10x - 6

%28x-3%29%2F%28x%5E3%2Bx%5E2-10x-6%29

Write it as %28%28x-3%29%2F1%29%2F%28%28x%5E3%2Bx%5E2-10x-6%29%2F1%29



Multiply by %281%2F%28x-3%29%29%2F%281%2F%28x-3%29%29








1%2F%28%28x%5E3%2Bx%5E2-10x-6%29%2F%28x-3%29%29

The denominator is %28x%5E3%2Bx%5E2-10x-6%29%2F%28x-3%29%29

So we divide it out:

Either by long division or synthetic division:

            x² +  4x + 2          3|1  1  -10  -6
x - 3)x³ +  x² - 10x - 6           |   3   12   6 
      x³ - 3x²                      1  4    2   0 
           4x² - 10x              x² + 4x² + 2  
           4x² - 12x
                  2x - 6
                  2x - 6 


Therefore

1%2F%28%28x%5E3%2Bx%5E2-10x-6%29%2F%28x-3%29%29

becomes:

1%2F%28x%5E2%2B4x%2B2%29

Edwin