$x^2+5x+16$  

 $x^{2\ }+5x+6+\frac{10}{x+1}$  

 $x^{2\ }+5x+6+\frac{10}{x^3+6x^2+11x+16}$  

 $x-3+\frac{-9x-4}{2x^2+x}$  

 $x-3+\frac{-3x+4}{2x^2+x}$  

 $x-5+\frac{-x+4}{2x^2+x}$  

 $x-5+\frac{-11x-4}{2x^2+x}$  

(x-3) is a factor of (x³ - 3x² + 2x + 2)

(x-3) is not a factor of (x³ - 3x² + 2x + 2)

The remainder when (x³ - 3x² + 2x + 2) is divided by (x-3) is zero.

The remainder when (x³ - 3x² + 2x + 2) is divided by (x-3) is not zero. The remainder is 17.

12

0

-12

8

4

-4

8