If for two real constants a and b, the expression ax3 +

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If for two real constants a and b, the expression ax³ + 3x² - 8x + b is exactly divisible by (x + 2) and (x – 2), then

1. a = 2, b = 12
2. a = 12, b = 2
3. a = 2, b = –12
4. a = –2, b = 12

Correct Option: C

P (x ) = ax³ + 3x² – 8x + b
[∵ P (x) is div. by (x + 2) & (x –2)]
∴ P (–2) = –8a + 12 + 16 + b = 0
⇒ –8a + b + 28 = 0 ...(i)
⇒ P(2) = 8a + 12 – 16 + b = 2
⇒ 8a + b – 4 = 0 ...(ii)
By equation (i) + (ii)
2b + 24 = 0

⇒ b = -	24	= -12
	2

From equation (i),
– 8a – 12 + 28 = 0
⇒ –8a = –16 ⇒ a = 2