Question
Factorize: $\text{x}^2+5\sqrt{5}\text{x}+30$
✓
Answer
$\text{x}^2+5\sqrt{5}\text{x}+30$ Splitting the middle term, $=\text{x}^2+2\sqrt{5}\text{x}+3\sqrt{5}\text{x}+30$
$\big[\therefore5\sqrt{5}=2\sqrt{5}+3\sqrt{5} \ \text{also} \ 2\sqrt{5}\times3\sqrt{5}=30\big]$
$=\text{x}\big(\text{x}+2\sqrt{5}\big)+3\sqrt{5}\big(\text{x}+2\sqrt{5}\big)$
$=\big(\text{x}+2\sqrt{5}\big)\big(\text{x}+3\sqrt{5}\big)$
$\therefore\text{x}^2+5\sqrt{5}\text{x}+30$
$=\big(\text{x}+2\sqrt{5}\big)\big(\text{x}+3\sqrt{5}\big)$
$\big[\therefore5\sqrt{5}=2\sqrt{5}+3\sqrt{5} \ \text{also} \ 2\sqrt{5}\times3\sqrt{5}=30\big]$
$=\text{x}\big(\text{x}+2\sqrt{5}\big)+3\sqrt{5}\big(\text{x}+2\sqrt{5}\big)$
$=\big(\text{x}+2\sqrt{5}\big)\big(\text{x}+3\sqrt{5}\big)$
$\therefore\text{x}^2+5\sqrt{5}\text{x}+30$
$=\big(\text{x}+2\sqrt{5}\big)\big(\text{x}+3\sqrt{5}\big)$
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