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Remainder Theorem

If a polynomi...

Question

If a polynomial $2 x^{3} - 9 x^{2} + 15 x + p$ , when divided by $(x - 2)$ , leaves $- p$ as remainder, then $p$ is equal to :

A

- 16

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B

- 5

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C

20

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D

10

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Solution

The correct option is D $- 5$
$B y$ $r e m a i n d e r$ $t h e o r e m,$ $r e m a i n d e r$ $= f (2) = - p$
$∴$ $2 \times 2^{3}$ $- 9 \times 2^{2}$ $+ 15 \times 2$ $+ p = - p$
$∴$ $16 - 36 + 30 + p = - p$
$∴$ $2 p = - 10$
$∴$ $p = - 5$

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