x3 - x2 - x+1
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We have,
![\quad \: {x}^{3} - {x}^{2} - x + 1 \\ \\ = x( {x}^{2} ) - 1( {x}^{2} ) - 1(x) - 1( - 1) \\ \\ = {x}^{2} (x - 1) - 1(x - 1) \\ \\ = (x - 1)( {x}^{2} - 1) \\ \\ = (x - 1) \left[ {(x)}^{2} - {(1)}^{2} \right] \\ \\ = (x - 1) \left[ (x - 1)(x + 1)\right] \\ \\ = (x - 1)(x - 1)(x + 1) \\ \\ = {(x - 1)}^{2} (x + 1)](https://tex.z-dn.net/?f=+%5Cquad+%5C%3A+%7Bx%7D%5E%7B3%7D+-+%7Bx%7D%5E%7B2%7D+-+x+%2B+1+%5C%5C+%5C%5C+%3D+x%28+%7Bx%7D%5E%7B2%7D+%29+-+1%28+%7Bx%7D%5E%7B2%7D+%29+-+1%28x%29+-+1%28+-+1%29+%5C%5C+%5C%5C+%3D+%7Bx%7D%5E%7B2%7D+%28x+-+1%29+-+1%28x+-+1%29+%5C%5C+%5C%5C+%3D+%28x+-+1%29%28+%7Bx%7D%5E%7B2%7D+-+1%29+%5C%5C+%5C%5C+%3D+%28x+-+1%29+%5Cleft%5B+%7B%28x%29%7D%5E%7B2%7D+-+%7B%281%29%7D%5E%7B2%7D+%5Cright%5D+%5C%5C+%5C%5C+%3D+%28x+-+1%29+%5Cleft%5B+%28x+-+1%29%28x+%2B+1%29%5Cright%5D+%5C%5C+%5C%5C+%3D+%28x+-+1%29%28x+-+1%29%28x+%2B+1%29+%5C%5C+%5C%5C+%3D+%7B%28x+-+1%29%7D%5E%7B2%7D+%28x+%2B+1%29 "\quad \: {x}^{3} - {x}^{2} - x + 1 \\ \\ = x( {x}^{2} ) - 1( {x}^{2} ) - 1(x) - 1( - 1) \\ \\ = {x}^{2} (x - 1) - 1(x - 1) \\ \\ = (x - 1)( {x}^{2} - 1) \\ \\ = (x - 1) \left[ {(x)}^{2} - {(1)}^{2} \right] \\ \\ = (x - 1) \left[ (x - 1)(x + 1)\right] \\ \\ = (x - 1)(x - 1)(x + 1) \\ \\ = {(x - 1)}^{2} (x + 1)")
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