Question 977707
(2x^2-3x+8) / (x-2)
<PRE>

Start with this:

   _________
x-2)2x²-3x+8

x goes into 2x² 2x times because {{{2x^2/x=2x}}},
so put 2x above the line above -3x

   <u>     2x  </u>
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:

   <u>     2x  </u>
x-2)2x²-3x+8
    <u>2x²-4x</u>

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

   <u>     2x  </u>
x-2)2x²-3x+8
    <u>2x²-4x</u>
         x

Now bring down the next term +8

   <u>     2x  </u>
x-2)2x²-3x+8
    <u>2x²-4x</u>
         x+8

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

   <u>     2x+1</u>
x-2)2x²-3x+8
    <u>2x²-4x</u>
         x+8

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

   <u>     2x+1</u>
x-2)2x²-3x+8
    <u>2x²-4x</u>
         x+8
         <u>x-2</u>

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

   <u>     2x+1</u>
x-2)2x²-3x+8
    <u>2x²-4x</u>
         x+8
         <u>x-2</u>
          10

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

The answer is {{{2x+1+10/(x-2)}}}

Edwin</pre>