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Factorize:$x^2 - 2\sqrt{2}x- 30$
Given :
$x^2 - 2\sqrt{2}x- 30$
To do :
We have to factorize the given expression.
Solution :
$x^2 - 2\sqrt{2}x- 30=x^{2}-5 \sqrt{2} x+3 \sqrt{2} x-30$ [Since $-5 \sqrt{2} x+3\sqrt{2} x=-2 \sqrt{2} x$ and $-5 \sqrt{2} x\times3\sqrt{2} x=-30\times x^2$]
$=x(x-5 \sqrt{2})+3 \sqrt{2}(x-5 \sqrt{2})$
$=(x-5 \sqrt{2})(x+3 \sqrt{2})$
Hence, $x^2 - 2\sqrt{2}x- 30=(x-5 \sqrt{2})(x+3 \sqrt{2})$.
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