X^2 2√(2)x 30 =x^2 5√(2)x+3√(2)x 30 =x(x 5√(2))+3√(2)(x 5√(2)) =(x 5√(2))(x+3√(2)) ...

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Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise x2-...

Question

Factorise
$x^{2} - 2 \sqrt{2} x - 30$

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Solution

$x^{2} - 2 \sqrt{2} x - 30 = x^{2} - 5 \sqrt{2} x + 3 \sqrt{2} x - 30 = x (x - 5 \sqrt{2}) + 3 \sqrt{2} (x - 5 \sqrt{2}) = (x - 5 \sqrt{2}) (x + 3 \sqrt{2})$

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