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# How do you factor by grouping ${x^3} - {x^2} - x + 1$.

Last updated date: 26th Mar 2023
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Given expression is ${x^3} - {x^2} - x + 1$
We can write the above polynomial as ${x^2}(x - 1) - 1(x - 1)$
$\Rightarrow (x - 1)({x^2} - 1)$ $\because \left[ {{a^2} - {b^2} = (a + b)(a - b)} \right]$
$\Rightarrow (x - 1)(x - 1)(x + 1)$
$\therefore {x^3} - {x^2} - x + 1$ can be factorized into ${\left( {x - 1} \right)^2}(x + 1)$