`***`Lời giải`***`
a)
`P(x)=3x^3-x^5-5x^2+2x-x^4+1/2`
`=-x^5-x^4+3x^3-5x^2+2x+1/2`
`Q(x)=x^2+5x^5-7x-x^3-1/4`
`=5x^5-x^3+x^2-7x-1/4`
b)
`P(x)=-x^5-x^4+3x^3-5x^2+2x+1/2`
Hệ số cao nhất: `-1`
Hệ số tự do: `1/2`
`Q(x)=5x^5-x^3+x^2-7x-1/4`
Hệ số cao nhất: `5`
Hệ số tự do:`-1/4`
c)
`P(x)+Q(x)=-x^5-x^4+3x^3-5x^2+2x+1/2+5x^5-x^3+x^2-7x-1/4`
`=(5x^5-x^5)-x^4+(3x^3-x^3)+(x^2-5x^2)+(2x-7x)+(1/2-1/4)`
`=4x^5-x^4+2x^3-4x^2-5x+1/4`
`P(x)-Q(x)=-x^5-x^4+3x^3-5x^2+2x+1/2-(5x^5-x^3+x^2-7x-1/4)`
`=-x^5-x^4+3x^3-5x^2+2x+1/2-5x^5+x^3-x^2+7x+1/4`
`=(-x^5-5x^5)-x^4+(3x^3+x^3)+(-5x^2-x^2)+(2x+7x)+(1/2+1/4)`
`=-6x^5-x^4+4x^3-6x^2+9x+3/4`