Question

Divide using synthetic division: (2x^4+2x^3+-12x^2+x+6)/(x+3)​

Answer 1

Synthetic division yields

..... ||   2    2   -12    1      6  

-3  ||        -6    12    0    -3

= = = = = = = = = = = = = =

..... ||   2   -4     0    1      3

which translates to

$\dfrac{2x^4+2x^3-12x^2+x+6}{x+3}=2x^3-4x^2+1+\dfrac3{x+3}$