\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find the values of \(a\), \(b\), and \(c\) given the polynomial identity:$$ (x-1)(ax^2+bx+c) = 2x^3 - 5x^2 + 8x - 5, \forall x\in \mathbb{R} $$
\(a = \)
, \(b = \)
, \(c = \)