CMR (x-2)(x-4)(x-6)(x-8) + 16 > 0 với mọi x

$\quad (x-2)(x-4)(x-6)(x-8) +16$

$= (x^2 - 10x +16)(x^2 - 10x + 24)+16$

$= (x^2 -10x)^2 + 40(x^2 - 10x) + 384 + 16$

$= (x^2 -10x)^2 + 2.20(x^2 - 10x) + 400$

$= (x^2 - 10x + 20)^2 \geq 0\quad \forall x$

Vậy $(x-2)(x-4)(x-6)(x-8) +16\geq 0\quad \forall x$