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The quotient obtained when $x^{4} + 11 x^{3} - 44 x^{2} + 76 x + 48$ is divided by $x^{2} - 2 x + 1$ is

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$x^{2} + 13 x + 25$

$x^{2} - 13 x + 5$

$x^{2} - 13 x + 19$

$x^{2} + 13 x - 19$

answer is B.

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Detailed Solution

First equation $x^{2} - 2 x + 1$

$x^{2} = 2 x - 1$

By using Synthetic division

Coefficients of given equation

${Quotient = x^{2} + 13 x - 19}$

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