How to remainder theorem with a second degree divisor

Question

Example: If a polynomial g(x) = x³ +2x² + 2x + 3 is divided by (x-1)(x-2), then find the remainder using the remainder theorem.

Answer 1

I started to try to explain it, then I found a website that does a great job of explaining it:

 

techiemathteacher.com/2014/04/17/remainder-theorem-with-second-degree-divisor/

 

The key is to know that the answer will be of the form Ax + B  (not just a constant like with a linear divisor.)