Divide x2 - 2x2 - 5x + 6 by x-1 Divide 6x2 - 13x + 5 by 2x-1 Find the quotient when x3+x2-x-1 is divided by x-1

$$\begin{array}{c|cc cc} \multicolumn{2}{r}{x^2} & -x & -6 \\ \cline{2-5} x-1 & x^3 & -2x^2 & -5x & +6 \\ \multicolumn{2}{r}{-(x^3} & -x^2) \\ \cline{2-3} \multicolumn{2}{r}{0} & -x^2 & -5x \\ \multicolumn{2}{r}{} & -(-x^2 & +x) \\ \cline{3-4} \multicolumn{2}{r}{} & 0 & -6x & +6 \\ \multicolumn{2}{r}{} & & -(-6x & +6) \\ \cline{4-5} \multicolumn{2}{r}{} & & 0 & 0 \\ \end{array}$$

The quotient is $\boxed{x^2 - x - 6}$.

2. Divide $6x^2 - 13x + 5$ by $2x - 1$.

$$\begin{array}{c|cc cc} \multicolumn{2}{r}{3x} & -5 \\ \cline{2-4} 2x-1 & 6x^2 & -13x & +5 \\ \multicolumn{2}{r}{-(6x^2} & -3x) \\ \cline{2-3} \multicolumn{2}{r}{0} & -10x & +5 \\ \multicolumn{2}{r}{} & -(-10x & +5) \\ \cline{3-4} \multicolumn{2}{r}{} & 0 & 0 \\ \end{array}$$

The quotient is $\boxed{3x - 5}$.

3. Find the quotient when $x^3 + x^2 - x - 1$ is divided by $x - 1$.

$$\begin{array}{c|cc cc} \multicolumn{2}{r}{x^2} & +2x & +1 \\ \cline{2-5} x-1 & x^3 & +x^2 & -x & -1 \\ \multicolumn{2}{r}{-(x^3} & -x^2) \\ \cline{2-3} \multicolumn{2}{r}{0} & 2x^2 & -x \\ \multicolumn{2}{r}{} & -(2x^2 & -2x) \\ \cline{3-4} \multicolumn{2}{r}{} & 0 & x & -1 \\ \multicolumn{2}{r}{} & & -(x & -1) \\ \cline{4-5} \multicolumn{2}{r}{} & & 0 & 0 \\ \end{array}$$

The quotient is $\boxed{x^2 + 2x + 1}$.