what is the quotient of (x³ - 3x² + 3x - 2) ÷ (x² - x + 1)?\no x - 2\no x + 2\no x - 4\no x + 1

Explanation:

Step1: Divide leading terms

Divide $x^{3}$ by $x^{2}$, we get $x$.

Step2: Multiply and subtract

Multiply $x^{2}-x + 1$ by $x$: $x(x^{2}-x + 1)=x^{3}-x^{2}+x$. Subtract from $x^{3}-3x^{2}+3x - 2$: $(x^{3}-3x^{2}+3x - 2)-(x^{3}-x^{2}+x)=-2x^{2}+2x - 2$.

Step3: Divide new leading term

Divide $-2x^{2}$ by $x^{2}$, we get $- 2$.

Step4: Multiply and check remainder

Multiply $x^{2}-x + 1$ by $-2$: $-2(x^{2}-x + 1)=-2x^{2}+2x - 2$. Subtract from $-2x^{2}+2x - 2$: $(-2x^{2}+2x - 2)-(-2x^{2}+2x - 2)=0$.

Answer:

A. $x - 2$