`4`

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

`P(x)=2x^2 + x +4`

`b)P(0)=2*0^2 + 0 +4 = 4`

`P(-1)=2*(-1)^2 + (-1) +4 = 2 - 1 +4 = 1+4=5`

`P(1)=2*1^2 +1 +4 = 2+1+4=3+4=7`

`P(1/2)=2*(1/2)^2 + 1/2 +4 =2*1/4 + 1/2 +4 = 1/2 +1/2+4=1+4=5`

`5`

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

`P(x)=-3x+6`

`b)P(0)=-3*0+6=6`

`P(-1)=(-3)*(-1)+6=3+6=9`

`P(1/3)=(-3)*1/3+6 =-1+6=5`