What is the quotient of open paren x cubed minus 3 x squared plus 3 x minus 2 close paren divided by open paren x squared minus x plus 1 close paren ?

Divide the leading terms: x³ ÷ x² = x, so the quotient begins with x. Multiplying x(x² − x + 1) gives x³ − x² + x; subtracting leaves −2x² + 2x − 2. Then −2x² ÷ x² = −2, and −2(x² − x + 1) gives −2x² + 2x − 2, leaving no remainder. The quotient is x − 2, choice C.

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