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What must be subtracted to the polynomial $p (x) = 2 x 3 + 9 x 2 − 5 x − 15,$ so that the resulting polynomial is exactly divisible by $2 x + 3$ ?

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2

4

6

8

answer is C.

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Detailed Solution

Given polynomials are

p (x) = 2 x 3 + 9 x 2 − 5 x − 15

and

2 x + 3

. We need to find that what must be subtracted to the polynomial

p (x) = 2 x 3 + 9 x 2 − 5 x − 15,

so that the resulting polynomial is exactly divisible by

2 x + 3

.
We will use the long division method for performing the division.
We have,
Question Image

Since, the remainder is

6

, therefore

6

must be subtracted to the polynomial

p (x) = 2 x 3 + 9 x 2 − 5 x − 15,

so that the resulting polynomial is exactly divisible by

2 x + 3

.
Therefore, option 3 is correct.

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