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

-4

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-5

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-6

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-7

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Solution

The correct option is B
-5

Substitute x - 1 = 0 in the given polynomial

Remainder = 3 $\times$ 1-4 $\times$ 1-3 $\times$ 1-1= -5

Alternative

By division algorithm

$\begin{matrix} 3 x^{3} - x^{2} - x - 4 x - 1 3 x^{4} - 4 x^{3} - 3 x - 1 3 x^{4} - 3 x^{3} - --------- - - x^{3} - 3 x - 1 - x^{3} + x^{2} - -------- - - x^{2} - 3 x - 1 - x^{2} + x - ------- - - 4 x - 1 - 4 x + 4 - ------- - - 5 \end{matrix}$

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