The determinant - - a 2 -x ab ac ab b 2 -x bc ac bc c 2 -x is divisible by

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Addition of Vectors

The determina...

Question

The determinant $Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + x & a b & a c a b & b^{2} + x & b c a c & b c & c^{2} + x \end{matrix} ∣ ∣ ∣ ∣ ∣$ is divisible by

x

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x^{2}

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x^{3}

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none of these

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Δ =

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + x & a b & a c a b & b^{2} + x & b c a c & b c & c^{2} + x \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + x^{2} & a b & a c a b & b^{2} + x^{2} & b c a c & b c & c^{2} + x^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} (1 + x) & a b & a c a b & b^{2} (1 + x) & b c a c & b c & c^{2} (1 + x) \end{matrix} ∣ ∣ ∣ ∣ ∣

{log}_{e} (1 + x + x^{2} + x^{3}) = a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots

a_{1}

a_{2}

(x + 1)^{n} - x^{n} - 1

x^{3} + x^{2} + x,

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