Question:
Find the value
$x^{2}-2 \sqrt{2} x-30$
Solution:
Splitting the middle term,
$=x^{2}-5 \sqrt{2} x+3 \sqrt{2} x-30$
$[\therefore-2 \sqrt{2}=-5 \sqrt{2}+3 \sqrt{2}$ also $-5 \sqrt{2} \times 3 \sqrt{2}=-30]$
$=x(x-5 \sqrt{2})+3 \sqrt{2}(x-5 \sqrt{2})$
$=(x-5 \sqrt{2})(x+3 \sqrt{2})$
$\therefore x^{2}-2 \sqrt{2} x-30$
$=(x-5 \sqrt{2})(x+3 \sqrt{2})$
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