數學(A)

(5%) Given a basis $S = \{(t-1)^3, (t-1)^2, (t-1), 1\}$ of a vector space $\mathbf{P}_3(t)$ of polynomials of degree $\le 3$. If the coordinate of $x = 5t^3 - 4t^2 + 3t - 2$ with respect to $S$ is $(a,b,c,d)$, then $a+b+c+d = ?$