2x³-4x+7x²+7 divide by x²+2x-1

Rearrange 2x³-4x+7x²+7 in descending powers 2x³+7x²-4x+7 

Start with:
       _____________
x²+2x-1)2x³+7x²-4x+7

Divide:  2x³÷x² =  = 2x

Write 2x above -4x

                2x   
x²+2x-1)2x³+7x²-4x+7
     
Multiply 2x(x²+2x-1) = 2x³+4x²-2x and write
it below 2x³+7x²-4x and draw a line underneath

                2x   
x²+2x-1)2x³+7x²-4x+7
        2x³+4x²-2x

Subtract (2x³+7x²-4x)-(2x³+4x²-2x) = 2x³+7x²-4x-2x³-4x²+2x = 3x²-2x
Write that below the line and bring down the next (last) term +7: 


                2x   
x²+2x-1)2x³+7x²-4x+7
        2x³+4x²-2x
            3x²-2x+7
            
Divide:  3x²÷x² =  = 3

Write +3 above the 7:

                2x+3 
x²+2x-1)2x³+7x²-4x+7
        2x³+4x²-2x
            3x²-2x+7


Multiply 3(x²+2x-1) = 3x²+6x-3 and write
it below 2x³+7x²-4x and draw a line underneath


                2x+3 
x²+2x-1)2x³+7x²-4x+7
        2x³+4x²-2x
            3x²-2x+7
            3x²+6x-3
              

Subtract (3x²-2x+7)-(3x²+6x-3) = 3x²-2x+7-3x²-6x+3 = -8x+10

Write that below the line


                2x+3 
x²+2x-1)2x³+7x²-4x+7
        2x³+4x²-2x
            3x²-2x+7
            3x²+6x-3
               -8x+10

The answer is:  = 2x+3 + .

Edwin