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If x + 5 is a factor of the polynomial x3 + ax2 + ax - 15, then the value of a is:
1. -9
2. 7
3. 9
4. 8

1 Answer

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Correct Answer - Option 2 : 7

Given:

x + 5 is a factor of the polynomial x3 + ax2 + ax - 15

Concept:

If x + α is a factor of polynomial P(x), where 

P(x) = a1xn + a2xn - 1 + .......an - 1 + an 

Then

P(α) = 0

Calculation:

Let 

P(x) = x3 + ax2 + ax - 15

According to the question, x + 5 is a factor of a polynomial, hence

P(-5) = 0

⇒ (-5)3 + a(-5)2 + a(-5) - 15 = 0 

⇒ - 125 + 25a - 5a - 15 = 0

⇒ 20a = 140

⇒ a = 7

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