1. **State the problem:** Divide the polynomial $9x^3 - 2x^2 + 3x - 2$ by $x - 1$. 2. **Formula and rule:** Polynomial division can be done using long division or synthetic division. Here, we use long division. 3. **Set up the division:** Divide the leading term of the dividend $9x^3$ by the leading term of the divisor $x$ to get $9x^2$. 4. **Multiply and subtract:** Multiply $9x^2$ by $x - 1$ to get $9x^3 - 9x^2$. Subtract this from the original polynomial: $$ (9x^3 - 2x^2 + 3x - 2) - (9x^3 - 9x^2) = \cancel{9x^3} - 2x^2 + 3x - 2 - \cancel{9x^3} + 9x^2 = 7x^2 + 3x - 2 $$ 5. **Repeat the process:** Divide $7x^2$ by $x$ to get $7x$. 6. **Multiply and subtract:** Multiply $7x$ by $x - 1$ to get $7x^2 - 7x$. Subtract: $$ (7x^2 + 3x - 2) - (7x^2 - 7x) = \cancel{7x^2} + 3x - 2 - \cancel{7x^2} + 7x = 10x - 2 $$ 7. **Repeat again:** Divide $10x$ by $x$ to get $10$. 8. **Multiply and subtract:** Multiply $10$ by $x - 1$ to get $10x - 10$. Subtract: $$ (10x - 2) - (10x - 10) = \cancel{10x} - 2 - \cancel{10x} + 10 = 8 $$ 9. **Conclusion:** The quotient is $9x^2 + 7x + 10$ and the remainder is $8$. 10. **Final answer:** $$ \frac{9x^3 - 2x^2 + 3x - 2}{x - 1} = 9x^2 + 7x + 10 + \frac{8}{x - 1} $$