Divide the polynomial $x^{3} - 2 x^{2} - 4 x - 1$ by $x - 1$ and find the
remainder.

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Solution

$x^{2} - x - 5$
________
$x - 1) x^{3} - 2 x^{2} - 4 x - 1$
$x^{3} - x^{2}$
_
$- x^{2} - 4 x$
$- x^{2} + x$
__
$- 5 x - 1$
$- 5 x + 5$
_
$- 6$
_______
Remainder $= - 6$ .

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