First slide

Theory of expressions

Question

The value of k so that $x^{4} - 4 x^{3} + 5 x^{2} - 2 x + k$ is divisible by $x^{2} - 2 x + 2$ is

Moderate

A

0
B

–2
C

–1
D

2

Solution

$\begin{matrix} \begin{matrix} 2 \\ - 2 \end{matrix} \begin{matrix} 1 & - 4 & 5 & - 2 & k \\ 0 & 2 & - 4 & - 2 & 0 \\ 0 & 0 & - 2 & 4 & 2 \end{matrix} \\ \begin{matrix} 1 & - 2 & - 1 \end{matrix} \begin{matrix} 0 & k + 2 \end{matrix} \end{matrix}$
$k = - 2$

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