Giải thích các bước giải:
+)Để $P\in Z$
$\to x^4-3x^2+5\quad\vdots\quad x-3$
$\to (x^4-3^4)-3(x^2-3^2)+59\quad\vdots\quad x-3$
Vì $x^4-3^4\quad\vdots\quad x-3, x^2-3^2\quad\vdots\quad x-3$
$\to 59\quad\vdots\quad x-3$
$\to x-3\in\{59,1,-59,-1\}$
$\to x\in\{62,4,-56,2\}$
+)Để $Q\in Z$
$\to 2x^3+x^2+2x+13\quad\vdots\quad 2x-1$
$\to (2x^3-x^2)+(2x^2-x)+3x+13\quad\vdots\quad 2x-1$
$\to x^2(2x-1)+x(2x-1)+3x+13\quad\vdots\quad 2x-1$
$\to3x+13\quad\vdots\quad 2x-1$
$\to 2(3x+13)\quad\vdots\quad 2x-1$
$\to 6x+26\quad\vdots\quad 2x-1$
$\to 6x-3+29\quad\vdots\quad 2x-1$
$\to 3(2x-1)+29\quad\vdots\quad 2x-1$
$\to 29\quad\vdots\quad 2x-1$
$\to 2x-1\in\{1,29,-1,-29\}$
$\to 2x\in\{2,30,0,-28\}$
$\to x\in\{1,15,0,-14\}$