Answer:
[tex](i) P(\frac{1}{2}) = 2*(\frac{1}{2})^2 + 5*\frac{1}{2} -5[/tex]
[tex]=\frac{1}{2} +\frac{5}{2} -5\\\\=3-5 = -2[/tex]
[tex](ii) P(3) - Q(2) = 2(3^2)+5(3)-5 -[4(2^2) +3(2) +2][/tex]
[tex]= 18 + 15 -5 -16-6-2= 28-24 =4[/tex]
[tex](iii) P(x)\cdot Q(x) = (2x^2+5x-5)(4x^2-3x+2)[/tex]
[tex]=2x^2(4x^-3x+2) +5x(4x^2-3x+2)-5(4x^2-3x+2)\\\\=8x^4 -14x^3 -11x^2 -10x-20x^2+15x-10\\\\=8x^4 - 14x^3 -31x^2 +5 -10[/tex]
[tex](iv) P(x) + Q(x) = 2x^2 +5x -5 + 4x^2 -3x +2[/tex]
[tex]= 6x^2 +2x -3[/tex]
