The remainder when the polynomial $2 x^5-3 x^4+5 x^3-3 x^2+7 x-9$ is divided by $x^2-x-3$ is

The remainder when the polynomial $2 x^5-3 x^4+5 x^3-3 x^2+7 x-9$ is divided by $x^2-x-3$ is
  1. $-41 x-3$
  2. $41 x+3$
  3. $41 x-3$
  4. $-41 x+3$

Solution

$\begin{array}{r}\left.x^2-x-3\right) 2 x^5-3 x^4+5 x^3-3 x^2+7 x-9\left(2 x^3-x^2\right. \\ +10 x+4\end{array}$
$\therefore$ Remainder $=41 x+3$

Asked in: AP EAMCET 2022 (07 Jul Shift 1)

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