$x^3 - 4x = 0$
$x(x^2 - 4) = 0$
$x(x - 4)(x + 4) = 0$
$x_1 = 0$;
$x_2 - 4 = 0$
$x_2 = 4$;
$x_3 + 4 = 0$
$x_3 = -4$.

$x^4 - x^2 = 0$
$x^2(x^2 - 1) = 0$
$x^2(x - 1)(x + 1) = 0$
$x_1^2 = 0$
$x_1 = 0$;
$x_2 - 1 = 0$
$x_2 = 1$;
$x_3 + 1 = 0$
$x_3 = -1$.

$x^5 - 36x^3 = 0$
$x^3(x^2 - 36) = 0$
$x^3(x - 6)(x + 6) = 0$
$x_1^3 = 0$
$x_1 = 0$;
$x_2 - 6 = 0$
$x_2 = 6$;
$x_3 + 6 = 0$
$x_3 = -6$.

$9x^3 - x = 0$
$x(9x^2 - 1) = 0$
$x(3x - 1)(3x + 1) = 0$
$x_1 = 0$;
$3x_2 - 1 = 0$
$3x_2 = 1$
$x_2 = \frac{1}{3}$;
$3x_3 + 1 = 0$
$3x_3 = -1$
$x_3 = -\frac{1}{3}$.

$x^3 - 10x^2 + 25x = 0$
$x(x^2 - 10x + 25) = 0$
$x(x - 5)^2 = 0$
$x_1 = 0$;
$(x_2 - 5)^2 = 0$
$x_2 - 5 = 0$
$x_2 = 5$.

$x^3 + 2x^2 - 9x - 18 = 0$
$(x^3 + 2x^2) - (9x + 18) = 0$
$x^2(x + 2) - 9(x + 2) = 0$
$(x + 2)(x^2 - 9) = 0$
$(x + 2)(x - 3)(x + 3) = 0$
$x_1 + 2 = 0$
$x_1 = -2$;
$x_2 - 3 = 0$
$x_2 = 3$;
$x_3 + 3 = 0$
$x_3 = -3$.

$x^3 - 5x^2 + 4x - 20 = 0$
$(x^3 - 5x^2) + (4x - 20) = 0$
$x^2(x - 5) + 4(x - 5) = 0$
$(x - 5)(x^2 + 4) = 0$
$x_1 - 5 = 0$
$x_1 = 5$;
$x_2^2 + 4 = 0$
$x_2^2 ≠ -4$, поэтому уравнение имеет только один корень равный 5.

$x^5 - x^4 - x + 1 = 0$
$(x^5 - x^4) - (x - 1) = 0$
$x^4(x - 1) - (x - 1) = 0$
$(x - 1)(x^4 - 1) = 0$
$(x - 1)(x^2 - 1)(x^2 + 1) = 0$
$(x - 1)(x - 1)(x + 1)(x^2 + 1) = 0$
$x_1 - 1 = 0$
$x_1 = 1$;
$x_2 + 1 = 0$
$x_2 = -1$.