SOLUTION: Use polynomial long division to divide -9x3 – 18x2 – 11x – 2 by -3x2 – 5x – 2

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Question 530442: Use polynomial long division to divide
-9x3 – 18x2 – 11x – 2
by
-3x2 – 5x – 2
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Start with this:

         __________________
-3x²-5x-2)-9x³-18x²-11x - 2
        
Divide  getting 3x 
write 3x above the top line:

                     3x    
-3x²-5x-2)-9x³-18x²-11x - 2
          
Next multiply 3x by -3x²-5x-2, 3x(-3x²-5x-2), getting -9x³-15x-6x
and write this below and underline it like this:

                     3x    
-3x²-5x-2)-9x³-18x²-11x - 2
          -9x³-15x²- 6x
          
Next subtract (-9x³-18x²-11x)-(-9x³-15x²- 6x) =
               -9x³-18x²-11x+9x³+15x²+6x = -3x²-5x

and write that below the line:
            
                     3x    
-3x²-5x-2)-9x³-18x²-11x - 2
          -9x³-15x²- 6x
               -3x²- 5x 
               
Bring down the -2


                     3x    
-3x²-5x-2)-9x³-18x²-11x - 2
          -9x³-15x²- 6x
               -3x²- 5x - 2
               
Divide  getting +1 
write +1 above the top line:


                     3x + 1
-3x²-5x-2)-9x³-18x²-11x - 2
          -9x³-15x²- 6x
               -3x²- 5x - 2
          

Next multiply 1 by -3x²-5x-2, 1(-3x²-5x-2), getting -3x²-5x-2
and write this below and underline it like this:

                     3x + 1
-3x²-5x-2)-9x³-18x²-11x - 2
          -9x³-15x²- 6x
               -3x²- 5x - 2
               -3x²- 5x - 2 

Next subtract (-3x²-5x-2)-(-3x²-5x-2) =
               -3x²-5x-2+3x²+5x+2 = 0 

We write this 0 remainder down at the bottom

                     3x + 1
-3x²-5x-2)-9x³-18x²-11x - 2
          -9x³-15x²- 6x
               -3x²- 5x - 2
               -3x²- 5x - 2 
                          0

And that's it.  The answer is 3x + 1 with 0 remainder.

Edwin
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