Divide: $x^{6} - 1$ by $x^{3} - 2 x^{2} + 2 x - 1$

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Solution

Steps:
1) Multiply $(x^{3} - 2 x^{2} + 2 x - 1)$ with $x^{3}$ , to get $x^{6}$ , Remainder $= 2 x^{5} - 2 x^{4} + x^{3} - 1$
2) Multiply $(x^{3} - 2 x^{2} + 2 x - 1)$ with $2 x^{2}$ , to get $2 x^{5}$ , Remainder $= 2 x^{4} - 3 x^{3} + 2 x^{2} - 1$
3)Multiply $(x^{3} - 2 x^{2} + 2 x - 1)$ with $2 x$ to get $2 x^{4}$ , Remainder $= x^{3} - 2 x^{2} + 2 x - 1$
4) Multiply $(x^{3} - 2 x^{2} + 2 x - 1)$ with $1$ , to get $x^{3} - 2 x^{2} + 2 x - 1$ , remainder $= 0$

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