Question

solve sqrt2x2+7x+5sqrt2 by splitting the middle term

Answer 1

Use the given hint-

$5\sqrt{2}\times\sqrt{2}=10$
So pick two numbers such that they add up to $7$ and multiply to $10$ :
$2+5=7$ and $2*5=10$

Split the middle term as $2x+5x$ and factor :
$\sqrt{2}x^2\underbrace{+7x}+5\sqrt{2}$

$=\sqrt{2}x^2\underbrace{+2x+5x}+5\sqrt{2}$

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

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