Show that x-4 is a factor of x-2 2x-3 3x-4 x-4 2x-9 3x-16 x-8 2x-27 3x-64

[ | [ x 2 amp; 2x 3 amp; 3x 4; x 4 amp; 2x 9 amp; 3x 16; x 8 amp; 2x 27 ...

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Properties of Determinants

Show that x...

Question

Show that $x - 4$ is a factor of $∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣$

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If ⎛ ⎜ ⎝ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

then x

x

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

x

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

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