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ICSE Class 10 Mathematics Question 15 of 49

Multiple-Choice Questions — Question 15

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Question 15

If the polynomial 2x3 + 3x2 - 2x - 3 is completely divisible by (2x + a), and the quotient is equal to (x2 - 1), then one of the values of a is :

  1. -3

  2. -1

  3. 1

  4. 3

Answer

Given,

The polynomial 2x3 + 3x2 - 2x - 3 is completely divisible by (2x + a) and quotient is equal to (x2 - 1).

∴ 2x3 + 3x2 - 2x - 3 = (2x + a)(x2 - 1)

⇒ 2x3 + 3x2 - 2x - 3 = 2x3 - 2x + ax2 - a

⇒ 2x3 - 2x3 + 3x2 - 2x + 2x - 3 = ax2 - a

⇒ 3x2 - 3 = ax2 - a

From above equation,

a = 3.

Hence, Option 4 is the correct option.