Division and factorisation of polynomials
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Find the quotient when \({x^3} - {x^2} + x - 1\) is divided by \(x - 1\).
\begin{align}
&\begin{aligned}
&\qquad\; x^2+1\\
x-1&\sqrt{x^3-x^2+x-1}\\
&\quad \underline{x^3-x^2\qquad \qquad }\\
&\qquad\qquad\quad\;\; x-1\\
&\qquad\qquad\quad\;\; \underline{x-1\;}\\
&\qquad\qquad\qquad\;\;\; 0
\end{aligned}\\
\\
&\therefore x^3-x^2+x-1=(x-1)(x^2+1)\\
&\therefore \text{ Quotient is } x^2+1
\end{align}
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