$ P(x) = 2x^3 -2x + x^2 +3x+ 2 $
$ = 2x^3 + x^2 + (3x-2x) +2$
$ = 2x^3 +x^2 +x +2$
$ Q(x) = 4x^3 -3x^2 -3x +4x - 3x^3 +4x^2 +1$
$= (4x^3 -3x^3) - (3x^2 -4x^2) - (3x-4x) +1 $
$ = x^3 + x^2 + x +1$
$ Q(x) + R(x) = P(x)$
$\to R(x) = P(x) - Q(x) = (2x^3 +x^2 +x +2) - (x^3 + x^2 + x +1) $
$ = 2x^3 +x^2 +x +2 -x^3 -x^2 -x -1 $
$ = (2x^3 -x^3) + (x^2-x^2) + (x-1) + (2-1)$
$ = x^3+1$
Vậy $ R(x) = x^3+1$