Question

factorize xcube-2x square-5x+6

Answer 1

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Answer 2

$The \: \: answer \: \: is \: \: given \: \: below \\ \\ Now, \: \: {x}^{3} - 2 {x}^{2} - 5x + 6 \\ \\ = {x}^{3} - {x}^{2} - {x}^{2} + x - 6x + 6 \\ \\ = {x}^{2} (x - 1) - x(x - 1) - 6(x - 1) \\ \\ = (x - 1)( {x}^{2} - x - 6) \\ \\ = (x - 1)( {x}^{2} - 3x + 2x - 6) \\ \\ = (x - 1)(x(x - 3) + 2(x - 3)) \\ \\ = (x - 1)(x - 3)(x + 2), \\ \\ which \: \: is \: \: the \: \: required \: \: \\ factorization. \\ \\ PROCESS \: \: \\ \\ Put \: \: x = 1,2,3,4,... \\ \\ In \: \: this \: \: problem,\: \: x = 1 \: \: \\ satisfies \: \: the \: \: polynomial. \\ \\ So ,\: \: (x - 1) \: \: is \: \: taken \: \: as \: \: a \\ factor. \\ \\ Thank \: \: you \: \: for \: \: the \: \: question.$