Another way to find A (which is only another form of differentiation) is not to evaluate, that is reduce mod (x-a), like for B and C, but to reduce mod the high

Another way to find A (which is only another form of differentiation) is not to evaluate, that is reduce mod (x-a), like for B and C, but to reduce mod the higher-order term, (x+2)^2. The C term drops out immediately and (x-1)(x+2) = (x+2 - 3)(x+2) = -3(x+2) so we get 7x + 2 = -3A(x+2) + B(x-1) => (evaluate at x=1) => 9 = -9A