Factorize: x^2-22x-30 - Vidyadip

Question

Factorize:
$\text{x}^2-2\sqrt{2}\text{x}-30$

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Answer

$\text{x}^2-2\sqrt{2}\text{x}-30$
Splitting the middle term,
$=\text{x}^2=5\sqrt{2}\text{x}+3\sqrt{2}\text{x}-30$
$\big[\therefore-2\sqrt{2}=-5\sqrt{2}+3\sqrt{2} \ \text{also} \ -5\sqrt{2}\times3\sqrt{2}=-30\big]$
$=\text{x}\big(\text{x}-5\sqrt{2}\big)+3\sqrt{2}\big(\text{x}-5\sqrt{2}\big)$
$=\big(\text{x}-5\sqrt{2}\big)\big(\text{x}+3\sqrt{2}\big)$
$\therefore\text{x}^2-2\sqrt{2}\text{x}-30$
$=\big(\text{x}-5\sqrt{2}\big)\big(\text{x}+3\sqrt{2}\big)$

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