$5x^3 - 32x^2 + 75x - 71 = a(x - 2)^3 + b(x - 2)^2 + c(x - 2) + d$
$a(x - 2)^3 + b(x - 2)^2 + c(x - 2) + d = a(x^3 - 6x^2 + 12x - 8) + b(x^2 - 4x + 4) + cx - 2c + d = ax^3 - 6ax^2 + 12ax - 8a + bx^2 - 4bx + 4b + cx - 2c + d = ax^3 + x^2(b - 6a) + x(12a - 4b + c) + (-8a + 4b - 2c + d)$
Тогда:
$5x^3 = ax^3$
a = 5
 
$-32x^2 = (b - 6a)x^2$
−32 = b − 6a
b = −2
 
$75x = (12a - 4b + c)x^2$
75 = 12a − 4b + c
75 = 60 + 8 + c
c = 75 − 60 − 8
c = 7
 
−71 = −8a + 4b − 2c + d
−71 = −40 − 8 − 14 + d
d = −71 + 40 + 8 + 14
d = −9
Ответ: a = 5, b = −2, c = 7, d = −9.