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
