If the product $(3x^2 - 5x + 4)(7 - 2x)$ can be written in the form $ax^3 + bx^2 + cx + d$, where $a,b,c,d$ are real numbers, then find $8a

(3x^2  -  5x  +  4)    ( 7  -  2x)

7 ( 3x^2  -  5x  + 4)  =    21x^2  -35x  +  28

-2x ( 3x^2  -5x  + 4)  = -6x^3 + 10x^2  - 8x

Adding like terms  we  get

-6x^2  +  31x^2  - 43x + 28

a = -6       8a =  -48

b = 31      4b = 124

c =  -43    2c  = -86

d =  28

The answer is 18, actually.

\(8a+4b+2c+d=(3 \cdot (2)^2 - 5 \cdot (2) + 4)(7 - 2 \cdot (2)) = 6 \cdot 3 = \boxed{18}\)