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For which value of α, the expression 1 + x + x2 + 3x3 + x4 + α when divided by (x + 3) leaves no remainder?
1. -12
2. -5
3. -7
4. -9

1 Answer

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Correct Answer - Option 3 : -7

Concept:

No remainder means the number is completely divisible by the divisor.

Calculation:

∵ x + 3 completely divides the expression

∴ 1 + x + x2 + 3x3 + x4 + α = 0

When x = (-3)

⇒ 1 + (-3) + (-3)2 + 3(-3)3 + (-3)4 + α = 0

⇒ 1 – 3 + 9 – 81 + 81 + α = 0

⇒ 7 + α = 0

⇒ α = (-7)

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