Factors of $8 x^{2} - 9 x^{3} + 1$ are

(x - 1) (x^{2} + x + 1) (2 x - 1) (4 x^{2} + 2 x + 2)

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(x - 2) (x^{2} + x + 1) (2 x - 1) (4 x^{2} + 2 x + 2)

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(x + 1) (x - 1) (3 x - 3) (4 x + 4)

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(x - 1) (3 x + 2) (x + 2) (x + 2) (2 x - 1)

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Solution

The correct option is C $(x - 1) (x^{2} + x + 1) (2 x - 1) (4 x^{2} + 2 x + 2)$
$8 x^{2} - 9 x^{3} + 1 = 8 x^{6} - 8 x^{3} - x^{3} + 1$
$= 8 x^{3} (x^{3} - 1) - 1 (x^{3} - 1)$
$(x^{3} - 1) (8 x^{3} - 1)$
$(x - 1) (x^{2} + x + 1) (2 x - 1) (4 x^{2} + 2 x + 2)$

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A (x) = ∣ ∣ ∣ ∣ \begin{matrix} x + 1 & 2 x + 1 & 3 x + 1 2 x + 1 & 3 x + 1 & x + 1 3 x + 1 & x + 1 & 2 x + 1 \end{matrix} ∣ ∣ ∣ ∣

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