The expression that should be subtracted from $4 x^{4} - 2 x^{3} - 6 x^{2} + x - 5$ so that is may be exactly divisible by $2 x^{2} + x - 2$ is

3 x + 5

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- 3 x - 5

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- 3 x + 5

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3 x - 5

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Solution

The correct option is C $- 3 x - 5$

$2 x^{2} - 2 x$
$2 x^{2} + x - 2$ $4 x^{4} - 2 x^{3} - 6 x^{2} + x - 5$
$4 x^{4} + 2 x^{3} - 4 x^{2}$
$- 4 x^{3} - 2 x^{2} + x$
$- 4 x^{3} - 2 x^{2} + 4 x$
$- 3 x - 5$
Thus, $- 3 x - 5$ must be subtracted to make it exactly divisble

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