Bài giải:

5x³ – 32x² + 75x – 71 = a(x – 2)³ + b(x – 2)² + c(x – 2) + d

5x³ – 32x² + 75x – 71 = a(x³ – 6x² + 12x – 8) + b(x² -4x + 4) + c(x – 2) + d

5x³ – 32x² + 75x – 71 = ax³ + (-6a + b)x² + (12a – 4b + c)x – 8a + 4b – 2c + d

Suy ra: $\left\{ \begin{align}& a=5 \\ & -6a+b=-32 \\ & 12a-4b+c=75 \\ & -8a+4b-2c+d=-71 \\ \end{align} \right.$

$\Rightarrow $ $\left\{ \begin{align}& a=5 \\ & b=-2 \\ & c=7 \\ & d=-9 \\\end{align} \right.$

Vậy: a + b + c + d = 5 + (-2) + 7 + (-9) = 1.