Question

Create your own third degree polynomial that when divided by x + 2 has a remainder of –4.

Answer 1

Think of the inverse:

If a / b = c + (d/b) , then:
a = b * (c + d/b) = bc + bd
a = bc + bd


(x + 2) * (ax^2 + bx + c + (d/(x + 2)) = ?

Let's say that a = 1 , b = 2 , c = 3 , d = -4

(x + 2) * (x^2 + 2x + 3 - (4 / (x + 2)) =
(x + 2) * x^2 + (x + 2) * 2x + (x + 2) * 3 - (x + 2) * 4 / (x + 2) =
x^3 + 2x^2 + 2x^2 + 4x + 3x + 6 - 4 =
x^3 + 4x^2 + 7x + 2