1. **State the problem:** We need to divide the polynomial $6x^3 - 5x^2 - 2x + 1$ by a divisor using long division. Since the divisor is not specified, we assume the divisor is $x - a$ or a polynomial of lower degree. For demonstration, let's divide by $x - 1$. 2. **Set up the long division:** Divide $6x^3 - 5x^2 - 2x + 1$ by $x - 1$. 3. **Divide the leading terms:** $\frac{6x^3}{x} = 6x^2$. 4. **Multiply and subtract:** Multiply $6x^2$ by $x - 1$ to get $6x^3 - 6x^2$. Subtract this from the original polynomial: $$ (6x^3 - 5x^2 - 2x + 1) - (6x^3 - 6x^2) = (6x^3 - 6x^3) + (-5x^2 + 6x^2) - 2x + 1 = x^2 - 2x + 1 $$ 5. **Repeat the process:** Divide the new leading term $x^2$ by $x$ to get $x$. 6. **Multiply and subtract:** Multiply $x$ by $x - 1$ to get $x^2 - x$. Subtract: $$ (x^2 - 2x + 1) - (x^2 - x) = (x^2 - x^2) + (-2x + x) + 1 = -x + 1 $$ 7. **Repeat again:** Divide $-x$ by $x$ to get $-1$. 8. **Multiply and subtract:** Multiply $-1$ by $x - 1$ to get $-x + 1$. Subtract: $$ (-x + 1) - (-x + 1) = 0 $$ 9. **Conclusion:** The quotient is $6x^2 + x - 1$ and the remainder is $0$. **Final answer:** $$\frac{6x^3 - 5x^2 - 2x + 1}{x - 1} = 6x^2 + x - 1$$