Question

Factorize the given polynomial expression

$x^2-2\sqrt{2}x-30$

Answer 1

Given that,

$x^2-2\sqrt{2}x-30$

$=x^2-5\sqrt{2}+3\sqrt{2}x-(5\times 3\times 2)$

$=x^2-5\sqrt{2}+3\sqrt{2}x-\left(5\sqrt{2}\right)\left(3\sqrt{2}\right)$

$=x(x-5\sqrt{2})+3\sqrt{2}(x-5\sqrt{2})$

$=(x-5\sqrt{2})(x+3\sqrt{2})$

$\therefore x^2-2\sqrt{2}x-30=(x-5\sqrt{2})(x+3\sqrt{2})$