Given that \(128x^3-2(x+2)^3\) is exactly divisible by \(ax+4b\), where \(a\) and \(b\) are rational numbers. Use part (a), state the value of \(a\) and \(b\).[3]
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Answer:(a) \(2(3x-2)(21x^2+12x+4)\). (b) One pair: \(a=6,b=-1\); more generally \(a=3k,b=-k/2\), \(k\in\mathbb Q\setminus\{0\}\).