Question

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Answer 1

Let p(x) =  ax^3 + 9x^2 + 4x - 10

on dividing p(x) by (x+3) , 5 is the remainder.

p(x) would be div. by (x+3) if we subtract 5 from it.

Hence, x +3 is a factor of p(x) - 5

= x+3 is a factor of ax^3 + 9x^2 + 4x - 15

hence, x = - 3 is a solution of p(x) -5

so, a(-3)^3 + 9(-3)^2 + 4(-3) - 15 = 0

 -27a + 81  -12 -15 = 0

27a  = 54

a = 2  

hence, a = 2

Answer 2

Answer:

a = 2

Step-by-step explanation:

Let f(x) = ax³ + 9x² + 4x - 10.

By remainder theorem, if f(x) is divided by (x - a) then remainder is f(a).

Here, when f(x) is divided by (x + 3) the remainder is f(-3).

Given, remainder = 5.

Plug x = -3 in f(x) , we get

f(-3) = a(-3)³ + 9(-3)² + 4(-3) - 10

⇒ 5 = -27a + 81 - 12 - 10

⇒ 5 = -27a + 59

⇒ -54 = -27a

⇒ a = 2.

Therefore, the value of a = 2.

Hope it helps!