`a)`

`P(x)=2x^3 - 1/2 x - 2x^3 + 3/4 x^2 +5x+1`

`=(2x^3 - 2x^2) + 3/4 x^2 + (-1/2 x +5x) +1`

`=3/4 x^2 + 9/2 x +1`

`b)`

`Q(x)=-x^2 +4-6x^2 +3x - 3/5`

`=(-x^2 -6x^2) +3x + (4 - 3/5)`

`=-7x^2 +3x + 17/5`

`c)`

`N(x)=x^3 -x^2 +2x-3x^2 +5x-2`

`=x^3 + (-x^2 -3x^2) + (2x+5x)-2`

`=x^3 - 4x^2 +7x-2`

`d)`

`H(x)=5/4 x^3 + 1/3 x^2 - 7x^4 + 3/2 x^3 - 1/3 x^2 - 1`

`=-7x^4 + (5/4 x^3 + 3/2 x^3) + (1/3 x^2 - 1/3 x^2) - 1`

`=-7x^4 + 11/4 x^3 -1`.