Aby policzyć sumę współczynników wielomianu wystarczy policzyć u(1)
a)
[tex]u(x) = (2x^2-1)^2-(2x-1)^2[/tex]
[tex]u(1) = (2\cdot1^2-1)^2-(2\cdot1-1)^2= (2\cdot1-1)^2-(2-1)^2= (2-1)^2-1^2=\\\\1^2-1=1-1=0[/tex]
b)
[tex]u(x) = (x^2+8)(\sqrt8-x)(x+2\sqrt2)[/tex]
[tex]u(1) = (1^2+8)\cdot(\sqrt8-1)\cdot(1+2\sqrt2)=(1+8)(\sqrt8-1)(1+\sqrt8)=\\\\9\cdot(8-1)=9\cdot7=63[/tex]
c)
[tex]u(x) = (x-2)^3-(x-2)^2[/tex]
[tex]u(1) = (1-2)^3-(1-2)^2=(-1)^3-(-1)^2=-1-1=-2[/tex]
d)
[tex]u(x) = (x^2+x+1)(x^2-x+1)[/tex]
[tex]u(x) = (1^2+1+1)\cdot(1^2-1+1)= (1+1+1)\cdot(1-1+1)=3\cdot1=3[/tex]
