Question

Factorize...x^3+x^2-x+1

Answer 1

${x}^{3} + {x}^{2} - x + 1 \\ \\ factor \: out \: x {}^{2} \: from \: the \: given \: expression \\ \\ {x}^{2} (x - 1) - x + 1 \\ \\ extract \: the \: negative \: signs \: from \: the \: expression \\ \\ {x}^{2} (x - 1) - (x - 1) \\ \\ factor \: out \: (x - 1) \: from \: the \: expression \\ \\ (x - 1)( {x}^{2} - 1)$


$using \: the \: identity \: - - \\ {a}^{2} - {b}^{2} = (a - b)(a + b) \: to \: factor \: the \: expression \\ \\ (x - 1)( {x}^{2} - {1}^{2} ) \\ \\ (x - 1)(x - 1)(x + 1) \\ \\ (x - 1) {}^{2} (x + 1)$