Find the GCD of $(a^{3} - 4 a^{2} + 7 a - 6)$ and $(a^{3} - 5 a^{2} + 10 a - 8)$ by using the division method.

(a - 2)

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(a + 2)

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3 (a - 2)

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4 (a - 2)

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Solution

The correct option is A $(a - 2)$
$a^{3} - 5 a^{2} + 10 a - 8) a^{3} - 4 a^{2} + 7 a - 6 (1 a^{3} - 5 a^{2} + 10 a - 8 - + - + - --------------------- - a^{2} - 3 a + 2$

$a^{2} - 3 a + 2) a^{3} - 5 a^{2} + 10 a - 8 (a - 2 a^{3} - 3 a^{2} + 2 a - + - - -------------- - - 2 a^{2} + 8 a - 8 - 2 a^{2} + 6 a - 4 + - + - ------------------ - 2 a - 4$

$2 a - 4 = 2 (a - 2)$

$a - 2) a^{2} - 3 a + 2 (a - 1 a^{2} - 2 a - + - ------------- - - a + 2 - a + 2 + - - ---------- - 0$

So, GCD of $(a^{3} - 4 a^{2} + 7 a - 6)$ and $(a^{3} - 5 a^{2} + 10 a - 8)$ is $(a - 2) .$

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