Aby uporządkować wielomian korzystam ze wzorów skróconego mnożenia:
[tex](a-b)^{3} =a^{3} -3a^{2} b+3ab^{2} -b^{3} \\\\(a-b)(a+b)=a^{2} -b^{2} \\\\(a+b)^{2} =a^{2} +2ab+b^{2}[/tex]
[tex]W(x)=(x-2)^{3} -(2x+1)^{2} -(3x-2)(3x+2)\\\\W(x)=x^{3} -6x^{2} +12x-8-(4x^{2} +4x+1)-(9x^{2} -4)\\\\W(x)=x^{3} -6x^{2} +12x-8-4x^{2} -4x-1 -9x^{2} +4\\\\W(x)=x^{3} -19x^{2} +8x-5\\\\[/tex]
[tex]dla~~x=-\sqrt{2} \\\\W(-\sqrt{2} )=(-\sqrt{2} )^{3} -19\cdot (-\sqrt{2} )^{2} +8\cdot (-\sqrt{2} ) -5\\\\W(-\sqrt{2} )=-2\sqrt{2} -38 -8\sqrt{2} -5\\\\W(-\sqrt{2} )=-10\sqrt{2} -43[/tex]
