Wykonaj działania i uporządkuj otrzymany wielomian: [latex](x-5) ^{2} (x- sqrt{2} )+ x^{2} (2-x sqrt{2}) [/latex]

 [latex](x-5)^2(x- sqrt{2})+x^2(2-x sqrt{2})=[/latex][latex](x^{2}-10x+25)(x-sqrt{2})+x^{2}(2-xsqrt{2})[/latex][latex]=x^{3}-x^{2} sqrt{2}-10x^{2}+10x sqrt{2}+25x-25 sqrt{2} +2x^{2}-x^{3} sqrt{3}[/latex][latex]=(1- sqrt{2})x^{3}-(8+sqrt{2})x^{2}+(10sqrt{2}+25)x-25sqrt{2}[/latex]

[latex](x-5) ^{2} (x- sqrt{2} )+ x^{2} (2-x sqrt{2}) =\ =(x^2-10x+25)(x-sqrt2)+2x^2-sqrt2x^3=\ =x^3+sqrt2x^2-10x^2+10sqrt2x+25x-25sqrt2+2x^2-sqrt2x^3=\ =(1-sqrt2)x^3-(8+sqrt2)x^2+(10sqrt2+25)x-25sqrt2[/latex]