Polynomials

Let $f(x) = ax^3 + bx^2 + cx + d = (3x^2 - 5x + 4)(7 - x)$. Note that $8a + 4b + 2c + d = f(2)$, so hence we can just plug $x = 2$ into $(3x^2 - 5x + 4)(7 - x)$ for an answer of $$(3 \cdot 2^2 - 5 \cdot 2 + 4)(7 - 2) = (12 - 10 + 4)(7 - 2) = (6)(5) = \boxed{30}.$$