Question 443086
This is just a fancy way of them saying: DO LONG DIVISION. Then take your solution and multiply it by your dividend to get your original polynomial. So let's do it:

x-1 |  2x^3 -5x^2 + 8x -5

How many times does x go into 2x^3?  2x^2 times.

(x-1)*2x^2 = 2x^3 +2x^2

2x^3 -5x^2 + 8x -5
-(2x^3 -2x^2 +0 + 0)
--------------------
 0  -3x^2 + 8x - 5

How many times does x go into  -3x^2?  -3x times.

(x-1)*(-3x) = -3x^2 + 3x

-3x^2 +8x 0 -5
-(-3x^2 + 3x +0)
-----------------
   0   +5x - 5

How many times does x go into 5x?  5 times.

(x-1)*5 = 5x -5

5x-5
-(5x-5)
-------
0
---------


So we have our Q(x) + R = {{{(2x^2 -3x + 5)*(x-1)}}}

So then,  {{{highlight(2x^3 -5x^2 + 8  =  (2x^2-3x+5)*(x-1))}}}
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Let's check this

{{{2x^3 - 3x^2 +5x -2x^2 +3x -5 = 2x^3 -5x^2 +8x -5}}} Check.

So then our representation is correct.