Mathematics
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 :
-3
-1
1
3
Factorisation
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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.
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