Question
Factorize:
$2\text{x}^2+3\sqrt{5}\text{x}+5$
$2\text{x}^2+3\sqrt{5}\text{x}+5$
✓
Answer
$2\text{x}^2+3\sqrt{5}\text{x}+5$
Splitting the middle term,
$=2\text{x}^2+2\sqrt{5}\text{x}+\sqrt{5}\text{x}+5$
$=2\text{x}\big(\text{x}+\sqrt{5}\big)+\sqrt{5}\big(\text{x}+\sqrt{5}\big)$
$=\big(\text{x}+\sqrt{5}\big)\big(2\text{x}+\sqrt{5}\big)$
$\therefore2\text{x}^2+3\sqrt{5}\text{x}+5$
$=\big(\text{x}+\sqrt{5}\big)\big(2\text{x}+\sqrt{5}\big)$
Splitting the middle term,
$=2\text{x}^2+2\sqrt{5}\text{x}+\sqrt{5}\text{x}+5$
$=2\text{x}\big(\text{x}+\sqrt{5}\big)+\sqrt{5}\big(\text{x}+\sqrt{5}\big)$
$=\big(\text{x}+\sqrt{5}\big)\big(2\text{x}+\sqrt{5}\big)$
$\therefore2\text{x}^2+3\sqrt{5}\text{x}+5$
$=\big(\text{x}+\sqrt{5}\big)\big(2\text{x}+\sqrt{5}\big)$
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