Ta có
$f(x) = x^{20} - 10x^{19} + 10x^{18} - 10x^{17} + \cdots + 10x^2 - 10x + 1$
$= x^{20} - 9x^{19} -x^{19} + 9x^{18} + x^{18} - 9x^{17} -x^{17} + \cdots + x^2 - 9x - x + 9 -8$
$= x^{19} (x-9) - x^{18} (x-9) + x^{17}(x-9) - \cdots + x(x-9) -(x-9) - 8$
$= (x-9)(x^{19} - x^{18} + x^{17} - \cdots + x - 1) - 8$
Khi đó
$f(9) = 0 (x^{19} - x^{18} + x^{17} - \cdots + x - 1) - 8$
$= -8$
Vậy $f(9) = -8$.