Question

Factor x3 + x2 + x + 1 by grouping resulting expression​

Answer 1

Answer:

$(x + 1)(x {}^{2} + 1)$

Step-by-step explanation:

$x {}^{3} + 1 + {x}^{2} + x \\ x {}^{3} + {1}^{3} + {x}^{2} + x \\ by \: using \: identity : \\ a {}^{3} + b {}^{3} = (a + b)(a {}^{2} + b {}^{2} - ab) \\ \\ (x + 1)( {x}^{2} + 1 {}^{2} - x \times 1) + x {}^{2} + x\\ taking \: x \: common : \\ (x + 1)( {x}^{2} + 1 {}^{2} - x ) + x(x + 1) \\ taking \: (x + 1) \: common : \\ (x + 1)( {x}^{2} + 1 {}^{2} - x + x) \\ (x + 1)( {x}^{2} + 1)$