Factorize: 55x^2+20x+35 - Vidyadip

Question

Factorize: $5\sqrt{5}\text{x}^2+20\text{x}+3\sqrt{5}$

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Answer

$5\sqrt{5}\text{x}^2+20\text{x}+3\sqrt{5}$
Splitting the middle term, $=5\sqrt{5}\text{x}^2+15\text{x}+5\text{x}+3\sqrt{5}$
$\big[\therefore20=15+5 \ \text{and} \ 15\times5=5\sqrt{5}\times3\sqrt{5}\big]$
$=5\text{x}\big(\sqrt{5}\text{x}+3\big)+\sqrt{5}\big(\sqrt{5}\text{x}+3\big)$
$=\big(\sqrt{5}\text{x}+3\big)\big(5\text{x}+\sqrt{5}\big)$
$\therefore5\sqrt{5}\text{x}^2+20\text{x}+3\sqrt{5}$
$=\big(\sqrt{5}\text{x}+3\big)\big(5\text{x}+\sqrt{5}\big)$

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