x^2+3√(3)x+6 = x^2 + √(3)x +2 √(3)x +6 = x(x+√(3))+2√(3)(x+√(3)) = (x+√(3))(x+2√(3)) ...

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Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise: x2...

Question

Factorise:
$x^{2} + 3 \sqrt{3} x + 6$

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Solution

$x^{2} + 3 \sqrt{3} x + 6 = x^{2} + \sqrt{3} x + 2 \sqrt{3} x + 6 = x (x + \sqrt{3}) + 2 \sqrt{3} (x + \sqrt{3}) = (x + \sqrt{3}) (x + 2 \sqrt{3})$

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