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If $2 x^{3} - a x^{2} - 5 x + 6$ is exactly divided by $x - 3$ , then the polynomial is

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$2 x^{3} + 5 x^{2} - 5 x + 6$

$2 x^{3} + 5 x^{2} + 5 x - 6$

$2 x^{3} - 5 x^{2} - 5 x + 6$

$2 x^{3} + 5 x^{2} + 5 x + 6$

answer is C.

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Detailed Solution

$f (3) = 0$

$\Rightarrow 2 {(3)}^{3} - a {(3)}^{2} - 5 (3) + 6 = 0$

$54 - 9 a - 15 + 6 = 0$

$- 9 a = - 45$

$a = 5$

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