`a)`
`P(x)=x^5 - 3x^2 + 7x^4 - 9x^3 + x^2 - (1)/(4)x`
`=x^5 + 7x^4 - 9x^3 + (x^2 - 3x^2) - (1)/(4)x`
`=x^5 + 7x^4 - 9x^3 - 2x^2 - (1)/(4)x`
`Q(x)=5x^4 - x^5 + x^2 - 2x^3 + 3x^2 - (1)/(4)`
`=-x^5 + 5x^4 - 2x^3 + (x^2 + 3x^2) - (1)/(4)`
`=-x^5 + 5x^4 - 2x^3 + 4x^2 - (1)/(4)`
`b)`
`P(x) + Q(x)`
`=(x^5+7x^4-9x^3-2x^2-(1)/(4)x)`
`+(-x^5+5x^4-2x^3+4x^2-(1)/(4))`
`=x^5+7x^4-9x^3-2x^2-(1)/(4)x-x^5+5x^4-2x^3+4x^2-(1)/(4)`
`=(x^5-x^5)+(7x^4+5x^4)+(-9x^3-2x^3)+(4x^2-2x^2)-(1)/(4)x-(1)/(4)`
`=12x^4 - 11x^3 + 2x^2 - (1)/(4)x - (1)/(4)`
`P(x) – Q(x)`
`=(x^5+7x^4-9x^3-2x^2-(1)/(4)x)`
`-(-x^5+5x^4-2x^3+4x^2-(1)/(4))`
`=x^5+7x^4-9x^3-2x^2-(1)/(4) x+x^5-5x^4+2x^3-4x^2+(1)/(4)`
`=(x^5 + x^5)+(7x^4-5x^4)+(2x^3-9x^3)+(-2x^2-4x^2)-(1)/(4)x+(1)/(4)`
`=2x^5+2x^4-7x^3-6x^2-1/4x+1/4`
`c)` `P(1)`
`= 1^5 + 7.1^4 - 9.1^3 - 2.1^2 - (1)/(4).1`
`= 1 + 7.1 - 9.1 - 2.1 - (1)/(4)`
`= 1 + 7 - 9 - 2 - (1)/(4)`
`= -3 - (1)/(4)`
`= -(12+1)/4`
`= (-13)/(4)`
`Q(0)`
`= -0^5 + 5.0^4 - 2.0^3 + 4.0^2 - (1)/(4)`
`= 0 + 5.0 - 2.0 + 4.0 - (1)/(4)`
`= 0+0-0+0-(1)/(4)`
`= (-1)/(4)`