Question

$x {}^{3} - 2 {x}^{2} - x + 2 =$
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Answer 1

Answer:

x = 1 is zeros of this polynomial. So (x - 1) is factor of this. i.e

${x}^{3} - {x}^{2} - {x}^{2} + x - 2x + 2 =$

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

$= (x - 1)( {x}^{2} - x - 2) =$

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

$(x - 1)(x(x - 2) + 1(x - 2)) =$

$(x - 1)(x - 2)(x + 1)$