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Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise: 7x...

Question

Factorise:
$7 x^{2} + 2 \sqrt{14} x + 2$

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Solution

$7 x^{2} + 2 \sqrt{14} x + 2 \Rightarrow 7 x^{2} + \sqrt{14} x + \sqrt{14} x + 2 \Rightarrow \sqrt{7} x (\sqrt{7} x + \sqrt{2}) + \sqrt{2} (\sqrt{7} x + \sqrt{2}) \Rightarrow (\sqrt{7} x + \sqrt{2}) (\sqrt{7} x + \sqrt{2}) \Rightarrow (\sqrt{7} x + \sqrt{2})^{2}$
Thus, $7 x^{2} + \sqrt{14} x + 2$ can be factorised as $(\sqrt{7} x + \sqrt{2}) (\sqrt{7} x + \sqrt{2})$

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