Factorize x^2 + (√(2x ))+ x + 2


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Question Number 174036 by nadovic last updated on 23/Jul/22

$Factorize x^{2} + \sqrt{2 x} + x + 2$
	Answered by dragan91 last updated on 23/Jul/22

	$x^{} = t^{2}$ $t^{4} + t \sqrt{2} + t^{2} + 2$ $t^{4} + 2 t \sqrt{2} - t \sqrt{2} + t^{2} + 2 =$ $t (t^{3} + {(\sqrt{2})}^{3}) + (t^{2} - t \sqrt{2} + 2) =$ $t (t + \sqrt{2}) (t^{2} - t \sqrt{2} + 2) + (t^{2} - t \sqrt{2} + 2) =$ $(t^{2} - t \sqrt{2} + 2) (t^{2} + t \sqrt{2} + 1)$ $(x - \sqrt{2 x} + 2) (x + \sqrt{2 x} + 1)$
	Commented by nadovic last updated on 23/Jul/22

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