Question

Factorise x3 - 23x2 + 142x - 120.
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Answer 1

${x}^{3} - 23 {x}^{2} + 142x - 120 \\ \\ = {x}^{3} - 22 {x}^{2} + 120x - {x}^{2} + 22x - 120 \\ \\ = x( {x}^{2} - 22x + 120) - 1( {x}^{2} - 22x + 120) \\ \\ = (x - 1)( {x}^{2} - 22x + 120) \\ \\ = (x - 1)( {x}^{2} - 12x - 10x + 120) \\ \\ (x - 1)(x(x - 12) - 10(x - 12)) \\ \\ = (x - 1)(x - 10)(x - 12)$

hope it helps