First slide

Theory of expressions

Question

The remainder when $2 x^{5} - 3 x^{4} + 5 x^{3} - 3 x^{2} + 7 x - 9$ is divisible by $x^{2} - x - 3$ is :

Moderate

A

$33 x + 4$
B

$41 x + 3$
C

$41 x + 44$
D

$33 x - 4$

Solution

$\begin{matrix} \begin{matrix} 1 \\ 3 \end{matrix} \begin{matrix} 2 & - 3 & 5 & - 3 & 7 & - 9 \\ 0 & 2 & - 1 & 10 & 4 & 0 \\ 0 & 0 & 6 & - 3 & 30 & 12 \end{matrix} \\ \begin{matrix} 2 & - 1 & 10 & 4 \end{matrix} \begin{matrix} 41 & 3 \end{matrix} \end{matrix}$
Remainder = $41 x + 3$

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