Respuesta :

alekos
                 x  -   2
              _______________
x^2-x+1 | x^3 - 3x^2 + 3x - 2                x^3 - x^2  +  x                        -------------- 
                       -2x^2 + 2x -2                       -2x^2 + 2x  - 2                       ------------------                                   0
Quotient = x - 2

The quotient when [tex](x^3-3x^2+3x-2)\div(x^2-x+1)[/tex] is [tex](x-2)[/tex].

Given :

Equation -

[tex]\dfrac{x^3-3x^2+3x-2}{x^2-x+1}[/tex]

Solution :

[tex]\dfrac{x^3-3x^2+3x-2}{x^2-x+1} = \dfrac{x^3-2x^2-x^2+2x+x-2}{x^2-x+1}[/tex]

[tex]= \dfrac{(x^2(x-2)-x(x-2)+1(x-2))}{x^2-x+1}[/tex]      ------ (1)

Now taking (x - 2) common from numerator in equation (1) we get,

[tex]= \dfrac{(x-2)(x^2-x+1)}{x^2-x+1}[/tex]

[tex]=(x-2)[/tex]

Therefore the quotient when [tex](x^3-3x^2+3x-2)\div(x^2-x+1)[/tex] is [tex](x-2)[/tex].

For more information, refer the link given below

https://brainly.com/question/1575906

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