Dane są wielomiany [latex]w(x)=x^{3}+4x^{2}+6 oraz g(x)=2x^{3}+3x^{2}+5[/latex]. Oblicz wartość wielomianu [latex]K(x)=W(x)-G(x) dla x=sqrt{2}-1[/latex]

[latex]W(x)=x^3+4x^2+6\G(x)=2x^3+3x^2+5\K(x)=W(x)-G(x)\x=sqrt{2}-1\K(x)=x^3+4x^2+6 -(2x^3+3x^2+5)\K(x)=x^3+4x^2+6 -2x^3-3x^2-5\K(x)= - x^3+x^2+1\K(x)=-(sqrt{2}-1)^3+(sqrt{2}-1)^2+1\K(x)=-((sqrt{2})^3-3(sqrt{2})^2cdot 1+3cdot sqrt{2}cdot 1^2-1^3)+(sqrt{2})^2-2cdot sqrt{2}+1+1\K(x)=-2sqrt{2}+6-3sqrt{2}+1+2-2sqrt{2}+2\K(x)=-7sqrt{2}+11[/latex]