derdegraads ; vierdegraads

$x^{3} = 4 x^{2} - 4 x$
$x^{3} - 4 x^{2} + 4 x = 0$
$x (x^{2} - 4 x + 4) = 0$
$x (x - 2) (x - 2) = 0$
$x = 0$ of $x = 2$

$x^{3} - 3 x^{2} = 4 x$
$x^{3} - 3 x^{2} - 4 x = 0$
$x (x^{2} - 3 x - 4) = 0$
$x (x - 4) (x + 1) = 0$
$x = 0$ of $x = 4$ of $x = ‐ 1$

$x^{4} + 9 x^{3} = 22 x^{2}$
$x^{4} + 9 x^{3} - 22 x^{2} = 0$
$x^{2} (x^{2} + 9 x - 22) = 0$
$x^{2} (x + 11) (x - 2) = 0$
$x = 0$ of $x = ‐ 11$ of $x = 2$

$x^{2} = 8 x - 16$ $x^{2} - 8 x + 16 = 0$ $(x - 4) (x - 4) = 0$ $x = 4$	$x^{4} - 3 x^{2} = 4$ $x^{4} - 3 x^{2} - 4 = 0$ $(x^{2} - 4) (x^{2} + 1) = 0$ $x = 2$ of $x = ‐ 2$
$x^{4} = 8 x^{2} - 16$ $x^{4} - 8 x^{2} + 16 = 0$ $(x^{2} - 4) (x^{2} - 4) = 0$ $x = 2$ of $x = ‐ 2$	$x^{6} + 7 x^{3} = 8$ $x^{6} + 7 x^{3} - 8 = 0$ $(x^{3} + 8) (x^{3} - 1) = 0$ $x = ‐ 2$ of $x = 1$

$4 \cdot 5 \cdot 6 \cdot 7 + 1 = 841 = 29^{2}$
$21 \cdot 22 \cdot 23 \cdot 24 + 1 = 225.025 = 505^{2}$

$x (x + 1) (x + 2) (x + 3) + 1$

$x^{4} + 6 x^{3} + 11 x^{2} + 6 x + 1$

$x^{4} + 6 x^{3} + 11 x^{2} + 6 x + 1 = {(x^{2} + 3 x + 1)}^{2}$