1/ $Q(x) + P(x) = ( -5x^3 + 8x^2 - \dfrac{1}{3} + x) + (-4x + 6x^2 - x^3 + 4)$
$= -5x^3 + 8x^2 - \dfrac{1}{3} + x - 4x + 6x^2 - x^3 + 4$
$= ( - 5x^3 - x^3) + (8x^2 + 6x^2) + (x-4x) - ( \dfrac{1}{3} - 4 ) $
$= -6x^3 + 14x^2 - 3x + \dfrac{11}{3}$
2/ $Q(x) - P(x) = (-4x + 6x^2 - x^3 + 4)- ( -5x^3 + 8x^2 - \dfrac{1}{3} + x) $
$ = -4x + 6x^2 - x^3 + 4 + 5x^3 - 8x^2 + dfrac{1}{3} - x$
$ = (5x^3 - x^3) + (-8x^2 + 6x^2) + (-x-4x) - (-\dfrac{1}{3} -4)$
$ = 4x^3 - 2x^2 - 5x + \dfrac{13}{3}$