What should be added in the polynomial $x^{2} - 2 x^{2} - 3 x - 4$ so that it is completely divisble by $x^{2} - x$ ?

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Solution

$x^{2} - x) x^{3} - 2 x^{2} - 3 x - 4 (x - 1 x^{3} - x^{2}- x^{2} - 3 x - x^{2} - x- 4 x - 4$

$(x^{2} - x) (x - 1) + [- 4 x - y] = x^{3} - 2 x^{2} - 3 x - 4$
$∴ [+ 4 x + 4)$ should be added to $x^{2} - 2 x^{2} - 3 x - 4$
to be divisible by $x^{2} - x$

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