[tex]x( {x}^{3} - {x}^{2} + x - 1) = x( {x}^{3} - {x}^{2} + x) - 1 \\ {x}^{4} - {x}^{3} + {x}^{2} - x = {x}^{4} - {x}^{3} + {x}^{2} - 1 \: \: | - ( {x}^{4} - {x}^{3} + {x}^{2} ) \\ - x = - 1 \: \: | \times ( - 1) \\ x = 1[/tex]
[tex] 1({1}^{3}-{1}^{2}+1-1)=1-1+1-1=0\\1({1}^{3}-{1}^{2}+1)-1=1-1+1-1=0[/tex]
