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
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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)
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4
So the answer is:
Or the answer in remainder format is:
2x^2+x+4 R 4