SOLUTION: (2x^2-3x+8) / (x-2)

Start with this:

   _________
x-2)2x²-3x+8

x goes into 2x² 2x times because ,
so put 2x above the line above -3x

        2x  
x-2)2x²-3x+8


Multiply 2x by x-2 getting 2x²-4x and put it underneath
2x²-3x and draw a line underneath it:

        2x  
x-2)2x²-3x+8
    2x²-4x

Now subtract (2x²-3x)-(2x²-4x) = 2x²-3x-2x²+4x = -3x+4x = x and
write that under the line:

        2x  
x-2)2x²-3x+8
    2x²-4x
         x

Now bring down the next term +8

        2x  
x-2)2x²-3x+8
    2x²-4x
         x+8

x goes into x 1 time because ,
so put +1 above the line above +8. [There MUST
ALWAYS BE a sign placed between every two terms.]

        2x+1
x-2)2x²-3x+8
    2x²-4x
         x+8

Multiply +1 by x-2 getting x-2, and write it underneath
x+8 and draw a line underneath it:

        2x+1
x-2)2x²-3x+8
    2x²-4x
         x+8
         x-2

Finally subtract (x+8)-(x-2) = x+8-x+2 = 10, so write 10
below the bottom line:

        2x+1
x-2)2x²-3x+8
    2x²-4x
         x+8
         x-2
          10

We place the remainder 10 over the divisor x-2 and add that fraction
to the quotient.

The answer is 

Edwin