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Q.

The remainder obtained when the polynomial $x^{4} - 3 x^{3} + 9 x^{2} - 27 x + 81$ is
divided by $x - 3$ is ____________

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answer is 81.

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Detailed Solution

$\begin{array}{rcl} f (x) & = & x^{4} - 3 x^{2} + 9 x^{2} - 27 x + 81 \\ f (3 & = & 81 - 81 + 81 - 81 + 81 = 81 \end{array}$

remainder 81

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