SOLUTION: I need help figuring this out with long divison...Thanks (2x^3 - 3x^2 + 2x -4 divided by x-2

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Question 77311This question is from textbook Elementary Algebra
: I need help figuring this out with long divison...Thanks
(2x^3 - 3x^2 + 2x -4 divided by x-2 This question is from textbook Elementary Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
what number multiplied by x gets you 2x^3? The answer is 2x^2. Place 2x^2 over 2x^3. Now multiply 2x^2 and x and place it underneath 2x^3. Multiply x by 5 and place it under 9x 

    _2x^2___________________
x-2 |2x^3 - 3x^2 + 2x - 4           
     2x^3 - 4x^2
    ----------------

Now subtract the second line from the first 


    _2x^2___________________
x-2 |2x^3 - 3x^2 + 2x - 4           
   -(2x^3 - 4x^2)
    ----------------
             x^2


Now what number multiplied by x gives you x^2? The answer is x. Place this number over -3x^2 and multiply it by (x-2). Place the product of 4(x-2) under x^2+2x and subtract 

    _2x^2_+__x _________________
x-2 |2x^3 - 3x^2 + 2x - 4           
   -(2x^3 - 4x^2)
    ----------------
             x^2 + 2x
           -(x^2 - 2x)
           ------------
                   4x - 4

Now what expression multiplies by x to get 4x? The answer is 4, so place this over 2x and multiply 2x(x-2). Place this product under 4x - 4 and subtract 

    _2x^2_+__x __+_4_______________
x-2 |2x^3 - 3x^2 + 2x - 4           
   -(2x^3 - 4x^2)
    ----------------
             x^2 + 2x
           -(x^2 - 2x)
           ------------
                   4x - 4
                 -(4x - 8)
               ------------
                        4

So the answer is:
2x%5E2%2Bx%2B4+%2B4%2F%28x-2%29
Or the answer in remainder format is:
2x^2+x+4 R 4