The remainder when $2 x^{3} - 3 x^{2} + 7 x + 5$ is divided by $2 x + 3$ is :

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Solution

The correct option is C $- 19$
Observing, the first term in the quotient will be $x^{2} .$
$x^{2} (2 x + 3)$ gives $2 x^{3} + 3 x^{2} .$
The remainder when this term is subtracted from the dividend is $- 6 x^{2} + 7 x + 5.$
Now, the second term in the quotient will be $- 3 x .$
$- 3 x (2 x + 3)$ gives $- 6 x^{2} - 9 x$ , which when subtracted from the dividend gives $16 x + 5$
Now, the third term in the quotient is $8$ , giving $8 (2 x + 3)$ as $16 x + 24$ and thus, the remainder to be $5 - 24$ i.e. $- 19.$

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The remainder when 2x3−3x2+7x+5 is divided by 2x+3 is :

The remainder when $2 x^{3} - 3 x^{2} + 7 x + 5$ is divided by $2 x + 3$ is :