\(p(x)=2x^3+5x^2+4x+a,\qquad q(x)=4x^2+3ax+b.\)

Given that \(p(x)\) has a remainder of 2 when divided by \(2x+1\) and that \(q(x)\) is divisible by \(x+2\),

(i) find the value of each of the constants \(a\) and \(b\).

Given that \(r(x)=p(x)-q(x)\), and using your values of \(a\) and \(b\),

(ii) find the exact remainder when \(r(x)\) is divided by \(3x-2\).