Question

The polynomials ax^3 + 3x^2 - 13 and 2x^3 - 5x + a
are divided by (x + 2). If the remainder in each
case is same, then find the value of a.​

Answer 1

p(x) = ax^3 + 3x^2 - 13 and q(x) = 2x^3 - 5x + a

when p(x) & q(x) are divided by x + 2 = 0 ⇒ x = -2

p (-2) = q(-2)  [Remainders are same]

⇒ a(-2)3 + 3(-2)2 - 13 = 2 (-2)3 - 5(-2) + a

⇒ -8a + 12 - 13 = - 16 + 10 + a  

⇒ -9a = - 5  

⇒ a = 5/9

Hope this helps!