Find the value of \(a\) for which \(2x-3\) is a factor of \(\mathrm{P}(x)=2x^3-5x^2+ax+6\), where \(a\) is an integer. Hence, determine whether \(x+2\) is a factor of \(\mathrm{P}(x)\).[4]
Factorise \(\mathrm{P}(x)\) completely.[2]
Using your answers in (b), solve the equation \(2^{3y+1}-5(2^{2y})=2^y-6\).[3]
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Answer:(a) \(a=-1\); \(x+2\) is not a factor. (b) \((2x-3)(x-2)(x+1)\) (c) \(y=0.585\) or \(1\).