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Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise x2+...

Question

Factorise
$x^{2} + \sqrt{2} x - 24$

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Solution

$x^{2} + \sqrt{2} x - 24 = x^{2} + 4 \sqrt{2} x - 3 \sqrt{2} x - 24 = x (x + 4 \sqrt{2}) - 3 \sqrt{2} (x + 4 \sqrt{2}) = (x + 4 \sqrt{2}) (x - 3 \sqrt{2})$

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