Question:
Factorize:
$5 \sqrt{5} x^{2}+20 x+3 \sqrt{5}$
Solution:
We have:
$5 \sqrt{5} x^{2}+20 x+3 \sqrt{5}$
We have to split 20 into two numbers such that their sum is 20 and their product is 75.
Clearly,
$15+5=20$ and $15 \times 5=75$
$\therefore 5 \sqrt{5} x^{2}+20 x+3 \sqrt{5}=5 \sqrt{5} x^{2}+15 x+5 x+3 \sqrt{5}$
$=5 x(\sqrt{5} x+3)+\sqrt{5}(\sqrt{5} x+3)$
$=(\sqrt{5} x+3)(5 x+\sqrt{5})$
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