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. Subtract x(x² − x + 1) from the numerator to get −2x² + 2x − 2. Then divide the leading terms again: −2x² ÷ x² = −2; subtracting −2(x² − x + 1) leaves a remainder of 0. The quotient is x − 2, choice A.

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