Factorize:x^2+62x+10 - Vidyadip

Question

Factorize:$\text{x}^2+6\sqrt{2}\text{x}+10$

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Answer

$\text{x}^2+6\sqrt{2}\text{x}+10$Splitting the middle term,
$=\text{x}^2+5\sqrt{2}\text{x}+\sqrt{2}\text{x}+10$
$\big[\therefore6\sqrt{2}=5\sqrt{2}+\sqrt{2} \ \text{and} \ 5\sqrt{2}\times\sqrt{2}=10\big]$
$=\text{x}\big(\text{x}+5\sqrt{2}\big)+\sqrt{2}\big(\text{x}+5\sqrt{2}\big)$
$=\big(\text{x}+5\sqrt{2}\big)\big(\text{x}+\sqrt{2}\big)$
$\therefore\text{x}^2+6\sqrt{2}\text{x}+10$
$=\big(\text{x}+5\sqrt{2}\big)\big(\text{x}+\sqrt{2}\big)$

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