Question: Find the value
$2 x^{2}+3 \sqrt{5} x+5$
Solution:
Splitting the middle term,
$=2 x^{2}+2 \sqrt{5} x+\sqrt{5} x+5$
$=2 x(x+\sqrt{5})+\sqrt{5}(x+\sqrt{5})$
$=(x+\sqrt{5})(2 x+\sqrt{5})$
$\therefore 2 x^{2}+3 \sqrt{5} x+5$
$=(x+\sqrt{5})(2 x+\sqrt{5})$
